The US has been carrying out joint military exercises for years in the region as a signal of its military alliance with Seoul, and as a show of strength against North Korean aggression.

Mr Trump was unapologetic when he revealed the end of "war games" in the region, insisting that the North Koreans had given up more than the Americans to reach a deal.

The US president said in a press conference after the Singapore summit: “It is a very great day, it is a very great moment, in the history of the world.”

He predicted Kim would start denuclearise “very quickly” and revealed that the North Korean leader had already agreed to destroy a missile engine testing site.

Historic agreement

The climax of Mr Trump’s meeting with Kim - the first between a sitting North Korean and American leader - was the signing of a joint agreement.

The 400-word statement followed more than four hours of talks, first between the leaders one-on-one and then with a wider group of advisers.

It read: “President Trump and Chairman Kim Jong Un conducted a comprehensive, in-depth, and sincere exchange of opinions on the issues related to the establishment of new US-DPRK relations and the building of a lasting and robust peace regime on the Korean Peninsula.

“President Trump committed to provide security guarantees to the DPRK, and Chairman Kim Jong-un reaffirmed his firm and unwavering commitment to complete denuclearisation of the Korean Peninsula.”

Donald Trump speaks to the media in an hour-long Press conference credit: SAUL LOEB /AFP

The Democratic People's Republic of Korea, or DPRK, is an alternative name for North Korea.

The statement went on to list four specific pledges that both Mr Trump and Kim agreed to stand by.

The first was that both countries would establish “new relations” in the pursuit of “peace and prosperity” - an attempt to draw a line under the insults and threats of last year.

The second said that America and North Korea would “join their efforts to build a lasting and stable peace regime on the Korean Peninsula”.

The third said that Kim’s regime “commits to work toward complete denuclearisation of the Korean Peninsula” - a key demand from the Americans.

And the fourth promised that the remains of fallen US soldiers who died fighting in the Korean War would be repatriated to the United States.

The hand of friendship? Kim Jong-un pats Donald Trump on the back as the pair leave the signing ceremony credit: SAUL LOEB /AFP

Concerns emerge

Mr Trump touted the agreement as “very comprehensive” and said that denuclearisation was “going to happen” at a press conference yesterday.

However critics questioned how watertight the assurances written in the agreement were and whether they were detailed enough.

The phrase “complete, verifiable, irreversible denuclearisation” did not appear in the document, despite the Americans insisting Kim agree to the objective.

There were also no specific promises about exactly what parts of his nuclear programme Kim would give up or when.

Signed and sealed: Donald Trump shows the document he and Kim Jong-un put their names to in Singapore credit: JONATHAN ERNST /Reuters

There is also the issue that Pyongyang frequently refers to denuclearisation of the “Korean Peninsula”, which would imply disarmament on all sides.

Mr Trump warned that denuclearisation takes a “long time scientifically” and repeatedly refused to give a timetable for developments.

However he said that economic sanctions would not be lifted nor a new US embassy established in Pyongyang until there was proof of denuclerisation.

Both the Americans and the North Koreans have committed to future talks, which will be led on the US side by Mike Pompeo, the secretary of state.

Mr Trump said he “absolutely” would invite Kim to the White House and expressed enthusiasm for visiting North Korea, but said no dates had been set.

Tremendous relationship

Mr Trump hailed his “tremendous” relationship with Kim and said he believed he could trust the North Korean leader after the pair met in Singapore.

The US president said their talks were “honest, direct and productive”, adding: “We got to know each other well in a very confined period of time.”

Asked if he trusted Kim, Mr Trump replied: “I do.” Pushed to explain, Mr Trump said: “I know when someone wants to deal and I know when they don’t.”

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Throughout the day both leaders displayed surprisingly warm body language towards each other, given that they spent most of the last year trading insults and threats.

At numerous points during the summit they were seen patting each other on the back or arm, smiling and laughing together and sharing compliments.

Mr Trump said Kim was “very talented”, noting how he had taken over the North Korean leadership while still in his twenties - though acknowledging that Kim had “run it tough”.

Mr Trump said: “Anyone can make war but only the most courageous can make peace.”

He later said in an interview about Kim: “He's got a great personality. He's a funny guy, he's very smart, he's a great negotiator. He loves his people, not that I'm surprised by that.”

Human rights

Mr Trump revealed he had discussed North Korea’s human rights record “relatively briefly” with Kim but came under pressure to show he took the issue seriously.

A 2014 report from a United Nations Human Rights Council commission found the regime had committed multiple violations including arbitrary detention, torture [and] executions.

Asked about human rights, Mr Trump said: “It was discussed relatively briefly compared to denuclearisation … They will be doing things. I think he wants to do things.”

History in the making: Kim Jong-un and Donald Trump look at each other before signing the document credit: JONATHAN ERNST /Reuters

Reporters repeatedly pressed the president to square his praise for the North Korean leader with what was happening in the country, including the imprisonment of political dissidents.

Mr Trump mentioned Otto Warmbier, the US college student who was imprisoned in North Korea and died shortly after his return to America last year.

The US president praised the relatives of Mr Warmbier and wondered whether the progress in talks could have happened without the tragedy, which cast a spotlight on the regime.

Elsewhere in his hour-long press conference, Mr Trump said he hoped an end to the Korean War, which is technically still running 68 years after it begun, could be secured soon.

Mr Trump also praised the leaders of Japan, South Korea and China as well as Kim himself for the progress made on the issue of denuclearisation.

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06:55PM Kim is a 'total weirdo', says Republican senator

While most of the reaction to the Singapore summit has been received positively, both Republican and Democratic senators' analysis has been lukewarm at best.

Republican senator Marco Rubio said on Twitter: "While I know the President of the United States is trying to butter him up to get a good deal, Kim Jong-un is not a talented guy.

"He inherited the family business from his dad and grandfather. He is a total weirdo who would not be elected assistant dog catcher in any democracy."

Marco Rubio credit: Matthew Pennington/AP

Senate Republican leader Mitch McConnell called the meeting a "major first step," in US-North Korea relations, but not a decisive one if North Korea does not follow through.

"The next steps in negotiations will test whether we can get to a verifiable deal," McConnell said on the Senate floor. He added, "We and our allies must be prepared to restore the policy of maximum pressure."

That was echoed by House Speaker Paul Ryan, who said, "There is only one acceptable final outcome: complete, verifiable, irreversible denuclearization."

Others were just puzzled by the vagueness of the leaders' initial agreement.

"It is difficult to determine what of concrete nature has occurred," said Senate Foreign Relations Committee Chairman Bob Corker.

Democrats were openly skeptical, saying Trump had already given up some American leverage by committing to halting U.S. military exercises with treaty ally South Korea.

05:59PM Israel links 'historic' meeting to Trump's stance on Iran

Israel hailed US President Donald Trump's summit on Tuesday with North Korean leader Kim Jong-un as "historic", linking the talks in Singapore to Washington's tough stance towards the Iranian nuclear programme.

"This is an important step in the effort to strip the Korean peninsula of nuclear weaponry," Prime Minister Benjamin Netanyahu said in a statement. "President Trump is also taking a firm stance against Iran's attempt to obtain nuclear weaponry, as well as its belligerence in the Middle East."

04:55PM The world reacts to the Trump-Kim meeting

World powers welcomed the summit between US President Donald Trump and North Korean leader Kim Jong Un on Tuesday.

Most cautioned that the summit in Singapore was only the first step in a long journey to full denuclearisation of the the Democratic People's Republic of Korea, or DPRK, as North Korea calls itself.

Here are some of the main reactions so far:

China

In Beijing, which is Pyongyang's sole major ally and main trading partner, Chinese Foreign Minister Wang Yi said the fact that the two leaders "can sit together and have equal talks has important and positive meaning, and is creating a new history."

Chinese Foreign Minister Wang Yi credit: AFP

"Resolving the nuclear issue, on the one hand of course is denuclearisation, full denuclearisation. At the same time, there needs to be a peace mechanism for the peninsula, to resolve North Korea's reasonable security concerns," Wang said.

Japan

Japanese Prime Minister Shinzo Abe saw the summit as a "first step" towards "complete denuclearisation" and "the comprehensive resolution of issues concerning North Korea."

Japan's Prime Minister Shinzo Abe speaks to media after Trump's news conference credit: Issei Kato/Reuters

Russia

Russian Foreign Minister Sergei Lavrov said that while "we have not yet seen the documents... the mere fact that this meeting took place is of course positive."

European Union

EU diplomatic chief Federica Mogherini praised the summit as a "crucial and necessary step to build upon the positive developments achieved in inter-Korean relations and on the peninsula so far."

The aim of the international community remained "the complete, verifiable and irreversible denuclearisation of the Korean Peninsula", she said.

"The joint statement signed by the US and DPRK leaders today gives a clear signal that this goal can be achieved."

Britain

British Foreign Minister Boris Johnson said in tweet that the talks had been "constructive" and "DPRK's commitment to complete denuclearisation of the Korean Peninsula is an important first step towards a stable and prosperous future."

Britain's Foreign Secretary Boris Johnson leaves Downing Street credit: Simon Dawson/Reuters

International Atomic Energy Agency (IAEA)

Yukiya Amano, the head of the UN's International Atomic Energy Agency, welcomed the "DPRK's commitment towards complete denuclearisation of the Korean Peninsula."

"The IAEA stands ready to undertake any verification activities in the DPRK that it may be requested to conduct by the countries concerned," Amano added.

Norway

Norway's foreign minister Ine Eriksen Soreide said that notwithstanding the "fundamentally positive" step the summit represented, it was now "that the largest part of the work actually begins."

Poland

Jacek Sasin, aide to Prime Minister Mateusz Morawiecki, said that "if as a result of the meeting, North Korea will abandon its nuclear aspirations and no longer threatens to launch an attack, it's very good."

President Andrzej Duda's chief of staff, Krzysztof Szczerski, hailed the summit as "spectacular" and a "triumph of diplomacy".

04:27PM NATO throw support behind Singapore summit

President Donald Trump's meeting in Singapore with North Korean leader Kim Jong -un was a historic summit, the head of the NATO alliance said on Tuesday, calling for a Korean peninsula free from nuclear weapons.

"NATO welcomes the historic summit," NATO Secretary-General Jens Stoltenberg said in a statement.

"NATO strongly supports all efforts leading towards the eventual denuclearisation of the Korean Peninsula," he said.

04:07PM 'Trump has already given up American leverage over North Korea'

Charles Schumer, the US Senate democratic leader, said Mr Trump has already given up American leverage over North Korea.

The New York Democrat said during a speech on the Senate floor that Mr Trump's meeting with Mr Kim might well have been "a reality show summit".

Mr Schumer spoke as Mr Trump celebrated the first meeting in history between a sitting US president and a North Korean leader.

But Mr Trump also faced mounting questions about whether or not he got too little and gave away too much - including an agreement to halt US military exercises with treaty ally South Korea.

He said if North Korea does not denuclearise, the "meeting alone will be a victory for North Korea and a defeat for the US".

03:34PM At a glance - best quotes from landmark day

After what has been hailed as a historic day, here are the most striking quotes from the Trump-Kim summit.

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03:22PM US Senate leader: America must be prepared to restore 'maximum pressure policy' if Mr Kim breaks deal

Mitch McConnell, the US Senate majority leader, has said he supports Trump's North Korea deal.

But he warned that America and its allies must be prepared to "restore a maximum pressure policy" if Kim Jong-un does not adhere to the agreement.

"If North Korea does not prove willing to follow through, we and our allies must be prepared to restore the policy of maximum pressure," McConnell said in remarks opening the Senate session.

02:35PM Who got the upper hand? Body language expert's analysis

In their first moments of meeting each other, Donald Trump and Kim Jong-un both sought to project a sense of command, but displayed some anxiety at the start of their high-stakes summit in Singapore.

Body language experts said that in the 13 seconds or so that the US president held on to the hand of Mr Kim for the first time, he projected his usual dominance by reaching out first, and patting the North Korean leader's shoulder.

Not to be outdone, Mr Kim firmly pumped Mr Trump's hand, looking him straight in the eye for the duration, before breaking off to face the media.

Here expert Judi James analyses the leaders' encounters today- and what their body language means.

02:26PM UN chief urges support for US-North Korea agreement

United Nations Secretary General Antonio Guterres has urged the international community to offer support on carrying out the agreement on steps toward denuclearisation between the United States and North Korea.

"Implementing today's and previous agreements reached, in accordance with relevant Security Council resolutions, will require patience and support from the global community,” UN spokesman Stephane Dujarric said in a statement.

12:47PM Boris Johnson hails 'important first step towards a stable and prosperous future'

Foreign Secretary Boris Johnson hailed the Singapore talks as an "important first step towards a stable and prosperous future" in a post on Twitter:

12:26PM Theresa May: North Korea has finally heeded the message

Prime Minister Theresa May has hailed the North Korea summit as an "important step for the region".

Her official spokesman said that Kim Yong-un's commitment to denuclearistation is a "signal they have finally heeded the message".

12:16PM EU hails Trump-Kim talks as 'crucial and necessary step'

The EU has praised the summit as a "crucial and necessary step", saying it indicated "complete denuclearisation" of the Korean peninsula could be achieved.

"This summit was a crucial and necessary step to build upon the positive developments achieved in inter-Korean relations and on the peninsula so far," the EU's diplomatic chief Federica Mogherini said in a statement.

12:10PM UN nuclear watchdog 'ready to help' North Korea denuclearisation

The UN nuclear watchdog has welcomed the joint statement of Donald Trump and Kim Jong-un and said it was prepared to undertake verification activities.

After Mr Trump and Mr Kim pledged to work towards complete denuclearisation, Director General Yukiya Amano said in a statement: "The International Atomic Energy Agency stands ready to undertake any verification activities in the DPRK (North Korea) that it may be requested to conduct by the countries concerned, subject to authorization by the IAEA’s Board of Governors."

11:55AM US forces have had 'no updated guidance' on 'war games' with South Korea

The US Forces Korea said it had received “no updated guidance” yet related to the regular so-called "war games" exercises with South Korea that President Donald Trump said he will stop, reports Asia Correspondent Nicola Smith.

“The USFK has received no updated guidance on execution or cessation of training exercise – to include this fall’s scheduled Ulchi Freedom Guardian,” it said in response to a question from South Korea’s Yonhap news agency.

The Ulchi Freedom Guardian exercise is the world’s largest annual computerised command and control drill, normally taking place in August or September. In 2017 some 50,000 South Korean soldiers took part, alongside 17,500 US troops.

“In coordination with our ROK (South Korean) partners, we will continue with our current military posture until we receive updated guidance from the Department of Defence (DOD) and/or Indo-Pacific Command (INDOPACOM),” the statement added.

11:49AM Mission accomplished: Trump leaves Singapore, saying 'there's nothing more we could have done'

Mr Trump is pictured here boarding Air Force One as he prepares to depart Singapore.

He told reporters he is leaving early because "there was nothing more we could have done".

US President Donald Trump boards Air Force One credit: JONATHAN ERNST /REUTERS

He waves to reporters as he leaves Singapore

Meanwhile, Mr Trump has done a television interview with Fox News in which he says the denuclearisation process is "really moving rapidly".

11:33AM South Korea hails 'huge step forward' - but seeks 'more clear understanding' of Trump's remarks

A statement from South Korean President Moon Jae-in says the Trump-Kim summit opens a new era of peace and cooperation. The statement did not address Trump's comments about the drills.

He said: "It is a great victory achieved by both the United States and the two Koreas, and a huge step forward for people across the world who long for peace," paying his "high compliments for the courage and determination" of Mr Kim and Mr Trump.

Seoul's presidential office said it was trying to discern the exact meaning and intent of Trump's comments.

A spokesman said: "At this moment, the meaning and intention of President Trump's remarks requires more clear understanding."

11:12AM Tim Stanley: Summit is triumph of charisma over state diplomacy

North Korea has made and broken promises before, so why wouldn’t it lie again? Because, Mr Trump told a Press conference in Singapore, “you have a different administration. A different President. A different Secretary of State. We get it done.”

In Trump’s worldview, leadership is about character, and the bigger the character, the greater the possibilities, writes The Telegraph's Tim Stanley. Click here to read more.

10:48AM Trump now eager to 'take it a little bit easy'

As he ended his lengthy Press conference, Mr Trump congratulated reporters and said he is eager to "take it a little bit easy" now that the highly anticipated summit is over.

Mr Trump said he "really believes" Mr Kim is going to make good on his promise to denuclearise.

Trump joked that he "might stand before you in six months and say, 'Hey, I was wrong.'" But he said: "I don't know that I'll ever admit that."

10:37AM At-a-glance summary of Trump's Press conference

If you didn't manage to follow Donald Trump's hour-long Press conference in its entirety, our US Editor, Ben Riley-Smith provides a handy summary here of the highlights.

10:16AM Trump 'will probably need another summit' with Kim

Donald Trump's Press conference has now been going for more than an hour - and he says he is accepting his last few questions.

He just revealed that he believes he will "probably need another summit or meeting" with Mr Kim.

Mr Trump added that he "talked up" North Korea's "real estate and beachside hotel opportunities" in Kim Jong Un meeting.

10:12AM Conflict with North Korea 'could lead to loss of tens of millions of lives'

Mr Trump has revealed that he believes a conflict involving North Korea could lead to the loss of tens of millions of lives in South Korea.

He said he did not want to be "threatening" to North Korea in his talks with Mr Kim.

Asked why he had previously threatened North Korea with "fire and fury", he said it was "appropriate" language at the time.

Donald Trump speaks during his Press conference that lasted more than an hour credit: JONATHAN ERNST /Reuters

10:00AM US 'being taken advantage of' by 'virtually every country' in G7

Mr Trump says that the US is "being taken advantage of" by virtually every country in the G7. Britain is one of those countries.

Yesterday, it emerged that Mr Trump had torn up a G7 agreement and lashed out at his allies as part of a demonstration of strength as he flew into Singapore.

09:52AM Trump halted 300 new 'disrespectful' sanctions on North Korea

Mr Trump said he halted plans last week for 300 new North Korea sanctions because they would have been "disrespectful" ahead of his meeting with Kim Jong-un.

09:50AM Ben Riley-Smith: Ending war games is 'remarkable'

By pledging that America will end its “very provocative” war games with South Korea, Mr Trump is publicly attacking his own administration’s policy for the last 18 months, says US Editor Ben Riley-Smith, adding that the move is "remarkable".

09:42AM Trump refuses to spell out timetable for denuclearisation

Asked how long it will take for Mr Kim to complete denuclearisation, Mr Trump refused to spell out a timetable.

He said "it takes a long time scientifically" to do so, adding that once the process of denuclearisation has started, "it's pretty much over".

Donald Trump answers questions in Singapore credit: JONATHAN ERNST /Reuters

09:38AM Kim Jong-un accepts invitation to visit White House

Mr Trump has said that Kim Jong-un has accepted his invitation to visit the White House "sometime in the future".

He added that he discussed human rights with the North Korean leader and will hold more conversations on that in the future.

09:28AM Trump vows to 'end the war games' on Korean peninsula

Mr Trump has vowed that the US will “end the war games” on the Korean peninsula.

He said he would like to bring US troops back from South Korea one day, but adds this is not on the table yet.

Donald Trump during a Press conference after his summit with Kim Jong-un credit: Susan Walsh /AP

Mr Trump said: "I'd like to be able to bring them home… I'd like to be able to end the war games… I think it's very provocative." He added that war games are “tremendously expensive”.

Asked if he trusts Mr Kim, Mr Trump said: “I do.”

09:26AM Trump: Kim has agreed to destroy 'major missile testing site'

Mr Trump says Kim Jong-un has agreed to destroy a "major missile testing site", but does not offer further details.

09:21AM 'We are ready to start a new history, to begin a new chapter between our nations'

Mr Trump said that Mr Kim has taken a "bold step towards a bright new future for his people".

Describing the talks as "unprecedented", he said: "This proves that real change is indeed possible."

He said: "My meting was honest, direct and productive. We got to know each other well... under very strong, strong circumstances

"We are ready to start a new history, to begin a new chapter between our nations."

He added: "The past does not have to define the future... adversaries can become friends."

He said there is "no limit to what North Korea" can achieve when it gives up its nuclear weapons.

Mr Trump added: "Anyone can make war, but only the most courageous can make peace."

Mr Trump talks up the end of the Korean War, saying: "Now we can all have hope that it will soon end".

09:17AM Trump begins talking: 'I stand before you to deliver a message of hope and vision'

As he begins his Press conference, Mr Trump says: "It's my honour today to address the people of the world following this historic summit.

"We've spent many intensive hours together and I think most have you have gotten the signed document... it's very comprehensive, it's going to happen.

"I stand before you to deliver a message of hope and vision."

09:09AM Key questions unanswered by Trump-Kim document

As we expect the Trump Press conference to start in a few minutes, US Editor Ben Riley-Smith poses the key questions that remain unanswered by the Trump-Kim document:

What security reassurances have exactly been given?

Was the issue of US troops leaving S Korean discussed?

What is the process for denuclearisation?

What does denuclearisation actually mean?

09:05AM Mike Pompeo speaks to South Korean counterparts

US Secretary of State Mike Pompeo has spoken to his Japanese and South Korean counterparts after President Donald Trump's summit with North Korean leader Kim Jong-un.

Pompeo tweeted shortly after the summit ended Tuesday that he'd telephoned South Korean Foreign Minister Kang Kyung-wha and Japanese Foreign Minister Taro Kono. The State Department released a photograph of Pompeo on the phone.

Pompeo says on Twitter he provided the diplomats with "a brief readout of today's meeting" between Trump and Kim.

08:47AM The stage is set: Donald Trump Press conference due to begin shortly

All eyes are on this stage in Singapore as Donald Trump prepares to begin a Press conference. We are expecting him to address the media - and the world - in the next few minutes.

Meanwhile, Kim Jong-un is reported to have already left Singapore's Sentosa island to return to North Korea.

08:36AM China suggests sanctions reduction could be considered for North Korea

China's Foreign Ministry has said that sanctions relief could be considered for North Korea, after Donald Trump and Kim Jong-un signed the deal. Ministry spokesman Geng Shuang made the comment at daily news briefing in Beijing.

08:15AM Analysis: Tim Stanley on what has been agreed

We’re about two thirds of the way through the day’s events: the leaders have met, had lunch and signed a communique. Now we await Donald Trump’s Press conference, at which he will debrief us: what was actually agreed?

In fact, we already know, because the President kindly held up the communique for the cameras after he signed it.

Mr Trump’s signature on the left always looks like it’s been faxed over by a madman – and it was scrawled in gold on the pens used by the two leaders, although, in an odd twist, a North Korean apparatchik replaced Kim’s at the last minute, presumably to avoid assassination by poison pen.

What has been agreed? The two countries say they will continue talking, a process that hinges on this quid pro quo: the US has “committed to provide security guarantees” in exchange for “complete denuclearization of the Korean peninsular.”

Reaction is mixed. Some say this isn’t much different from earlier communiques and that it’s missing the kind of language about verification that would make it truly tough. The difference between this and the agreements struck in the Nineties, of course, is the immediate presence of both leaders. Kim and Trump are personally involved, staking their reputations on the success of this agreement.

One final thought: there is no language about human rights. That's not the subject of this summit, it's true, but the classic conservative objection to North Korea is not just about arms control. It's about the regime's subjugation of its citizens.

08:05AM Full statement signed by two leaders

Here is the full text of the document signed by Donald Trump and Kim Jong-un around an hour ago:

Joint Statement of President Donald J Trump of the United States of America and Chairman Kim Jong-un of the Democratic People's Republic of Korea at the Singapore Summit

President Donald J Trump of the United States of America and Chairman Kim Jong-un of the State Affairs Commission of the Democratic People's Republic of Korea (DPRK) held a first, historic summit in Singapore on June 12, 2018.

President Trump and Chairman Kim Jong-un conducted a comprehensive, in-depth and sincere exchange of opinions on the issues related to the establishment of new US-DPRK relations and the building of a lasting and robust peace regime on the Korean Peninsula. President Trump committed to provide security guarantees to the DPRK, and Chairman Kim Jong-un reaffirmed his firm and unwavering commitment to complete denuclearisation of the Korean Peninsula.

Convinced that the establishment of a new US-DPRK relations will contribute to the peace and prosperity of the Korean peninsula and of the world, and recognizing that the mutual confidence-building can promote the denuclearization of the Korean Prenisinulsa, President Trump and Chairman Kim Jong-un start the following:

The US and the DPRK commit to establish new US-DPRK relations in accordance with the desire of the peoples of the two counties for peace and prosperity The US and DPRK will join their efforts to build a lasting and stable peace regime on the Korean Peninsula Reaffirming the April 27, 2018 Panmunjom Declaration, the DPRK commits to work toward complete denuclearisation of the Korean Peninsula The US and the DPRK commit to recovering POW/MIA remains, including the immediate repatriation of those already identified.

Having acknowledged that the US-DPRK simmit - the first in history - was an epochal event of great significance and overcoming decades of tensions and hostilities between the two counties and for the opening up of a new future, President Trump and Chairman Kim Jong-un commit to implement the stipulations in this joint statement fully and expediently. The US and the DPRK commit to hold follow-on negotiations led by the US Secretary of State Mike Pompeo, and relevant high-level DPRK official, at the earliest possible date, to implement the outcomes of the US-DPRK summit.

President Donald J Trump of the United States of America and Chairman Kim Jong-un of the State Affairs Commission of the Democratic People's Republic of Korea have committed to cooperate for the development of new US-DPRK relations and for the promotion of peace, prosperity, and security of the Korean Peninsula and of the world.

June 12, 2018

Sentosa Island

07:51AM After the talks... more talks

The joint document also says that US Secretary of State Pompeo and a senior North Korean official will hold follow-up talks as soon as possible.

07:40AM What the leaders have signed

The White House has yet to release the document's text. But it was photographed by the news media during a signing ceremony.

It shows the North Korean leader has committed to "complete denuclearisation of the Korean Peninsula".

A close-up shot of the document signed by the leaders credit: SAUL LOEB /AFP

However, the text made no mention of US demands for "complete, verifiable and irreversible denuclearisation" - which is jargon for scrapping weapons and committing to inspections - but did restate the vaguer commitment.

The document lays out four broad commitments. It says the sides "commit to establish new US-DPRK relations in accordance with the desire of the peoples of the two countries for peace and prosperity."

And it says they will commit to recovering the remains of prisoners of war and those missing in action.

07:31AM Kim commits to 'complete denuclearisation of Korean Peninsula'

Kim Jong-un has committed to "complete denuclearisation of the Korean Peninsula" in the joint text signed by him and Donald Trump, according to the AFP news agency. We are expecting to see the document in full in the next couple of hours.

07:16AM 'The world will see a major change' Trump and Kim's comments from signing ceremony

US President Donald Trump and North Korean leader Kim Jong-un have signed a “comprehensive” and “important” document, although there are still no details of what they have actually agreed to, reports Nicola Smith.

The two leaders signed the leather-bound documents with flourish in a post-lunch ceremony, shaking hands twice while smiling and thanking each other.

“We’re signing a very important document, a pretty comprehensive document, we’ve had a really great time together, a great relationship,” said Mr Trump. “We’re both very honoured to sign the document.”

Kim Jong-un and Donald Trump smile and shake hands after the document signing on Sentosa Island credit: Evan Vucci /AP

Kim was less talkative, appearing to allow Mr Trump to take the lead. However, speaking through an interpreter, he called the document “historic.”

He added: “The world will see a major change. I would like to express my gratitude to President Trump to make this meeting happen.”

The US president said the contents of the agreement would be revealed at a press conference later today. He refused to answer a question from a small pool of journalists in the room about whether the North Koreans had signed up to full denuclearisation.

When asked if he would invite Kim to the White House he said he “absolutely would”.

06:49AM China 'welcomes and supports talks'

Chinese foreign minister Wang Yi said China "welcomes and supports talks" between the leaders of North Korea and the US, China Correspondent Neil Connor reports from Beijing.

Mr Wang said "peaceful dialogue is the only right way to resolve the peninsula issue, and China will continue to play a unique and important role in it," Chinese media reported.

The comments were made just moments before the signing ceremony.

06:46AM Kim will be invited to White House

Mr Trump concludes the signing ceremony by saying he will invite Mr Kim to the White House.

06:45AM 'A very special bond'

Mr Trump says "we have developed a very special bond" and thanks "Chairman Kim". He said it worked out better for both of them than anyone had predicted.

06:43AM Kim: We are leaving the past behind

Mr Kim says "we are leaving the past behind" and thanks Mr Trump for making the summit happen.

The US president says they are starting the process of denuclearisation very quickly, but will not go into details of the letter.

06:40AM Leaders arrive for signing

And here come Mr Kim and Mr Trump, who calls it an "important and comprehensive" document.

06:23AM Preparations under way for signing

A room is being prepared for an official signing ceremony, which appears to be imminent.

06:17AM Document will 'pledge to keep momentum alive'

CNN is reporting that a ‘signing’ referenced by Trump will be a document from US and North Korea to acknowledge progress and a pledge to keep momentum alive. A US official declines to get ahead of president with hard specifics.

06:03AM Trump's stroll with Kim

The leaders are progressing to a signing ceremony shortly but nobody knows what they are signing yet, writes Nicola Smith in Singapore.

Trump and Kim took a short and awkward stroll after lunch, along a path next to the hotel. Their conversation looked stilted and was inaudible but at some point Trump appeared to be pointing to the plants in the garden while making comments to Kim.

He also showed Kim the interior of the presidential limousine.

Although they had the language barrier to contend with, there were no signs of the natural warmth that seemed to exist between Kim and South Korean President Moon Jae-in from the first moment they met in April. Speaking to reporters waiting at the end of the path, Trump said that lots of progress had been made.

05:49AM Trump and Kim seen walking together alone

This is typical Trump, bringing some theatrics to proceedings. It is still not known what they will be signing - or when.

05:43AM 'We are going right now for a signing'

There is nothing on the schedule between lunch and a press conference at 4pm - however Mr Trump has told reporters that "we are going right now for a signing".

According to CNN, he said: "A really fantastic meeting -- a lot of progress. Better than anybody could have expected Top of the line."

05:35AM Trump cracks a joke before lunch

President Donald Trump joked about his appearance as he prepared to sit down to lunch with North Korea's Kim Jong-un.

Mr Trump said to photographers at Tuesday's summit in Singapore: "Getting a good picture, everybody? So we look nice and handsome and thin? Perfect."

A video feed provided by the summit host showed Mr Trump, Mr Kim and their aides taking their places at a long table.

Mr Trump took his spot in the middle of the table, and Kim opposite him.

05:31AM Kim is 'winning the summit'

Filing from Singapore, the Telegraph's Tim Stanley believes Kim Jong-un is "winning the summit" so far.

It’s true that Donald Trump has secured a number of concessions from North Korea in exchange for political engagement: Hostage releases and a pledge to suspend the nuclear programme. But diplomacy is a propaganda war, and Kim has proven to be sophisticated at manipulating opinion.

U.S. President Donald Trump, second from left, and North Korean leader Kim Jong Un, fourth from right, arrive for a working lunch at Capella Hotel credit: AP

It began before the meeting with Mr Trump, when he left his hotel on Monday night to go for a waddle around Singapore. Kim was greeted with cheers; politicians asked for a selfie. Bearing in mind that he is a dictator with the power of life and death over millions (something he routinely exercises) this transformation into a happy tourist was remarkable – and continued the next morning when he met Mr Trump, the two men smiling and apparently at ease with one another. They shook hands standing in front of a row of flags, alternately American and North Korean.

Read the full story.

05:09AM Sides sit down for working lunch

The US and North Korean teams have broken for lunch, which is an elaborate fusion of western and Korean delicacies, writes Nicola Smith in Singapore.

A total of 15 people are sitting round the table at the Capella Hotel. Besides the negotiating teams currently thrashing out the details of a possible denuclearisation team, Kim’s younger sister, Kim Yo-jong, has been invited to the lunch, as has White House press secretary Sarah Huckabee Sanders.

On the US side, two of the officials involved in intricate back channel negotiations in the run up to the summit – Sung Kim, the US ambassador to the Philippines, and Matthew Pottinger, deputy assistant to the President for Asian affairs, will be present.

North Korea’s participants will include No Kwang Chol, minister of the People’s Armed Forces, Choe Son Hui, the vice-minister of foreign affairs and Han Kwang Sang, the director of the central committee of the Workers’ Party of Korea.

Lunch will begin with a conventional western starter of prawn cocktail and avocado salad, followed by some flavours of Asia in the form of green mango kerabu with honey lime dressing and fresh octopus, and “Oiseon”, a Korean stuff cucumber.

The main course will also strike a balance between Korean and Western tastes.

The diners will be treated to beef short rib confit, served with potato dauphinois and steamed broccolini, red wine sauce on the side.

Also on the menu is a combination of sweet and sour crispy pork and Yangzhou fried rice with homemade XO chilli sauce.

And, perhaps to cater to Kim’s palate, chefs have prepared “Daegu jorim”, a soy braised cod fish with radish and Asian vegetables.

If the participants still have space for dessert, dark chocolate tartlet ganache is on offer and, in a boost for Haagen Dazs’ global brand, their vanilla ice cream will be drizzled with cheery coulis.

04:33AM The menu for the working lunch

The sides will be breaking for lunch in a short while - and Mr Trump won't be able to have his usual burger.

04:15AM China baffled by Ivanka Trump's 'Chinese proverb'

Chinese social media users are scratching their heads over a "Chinese proverb" Donald Trump's daughter and advisor Ivanka posted to Twitter as her father prepared for his summit with North Korea's Kim Jong Un.

China's internet quickly lit up, puzzled rather than flattered by the reference.

"Our editor really can't think of exactly which proverb this is. Please help!" the news channel for Sina - the company behind Weibo, China's largest Twitter-like platform - wrote on its official social media account.

In thousands of comments on Weibo, users proferred scores of different suggestions without arriving at a consensus.

Some suggested the proverb "the foolish old man removed mountains" - a common phrase used to signify perseverance. It refers to a fable about a man who persisted in his attempt to level a mountain he found inconvenient by dogged digging.

Her mysterious proverb was panned on Weibo.

"She saw it in a fortune cookie at Panda Express," one user wrote.

04:11AM The view from North Korea

North Koreans, meanwhile, are yet to find out what's happened today.

04:09AM The view from South Korea

President Trump had a last minute phone call with Moon Jae-in, the South Korean president, on the eve of the summit, Nicola Smith reports.

On Tuesday morning President Moon expressed hope for the summit’s success, which he said would open a new era of a peaceful, nuclear-free Korean Peninsula, and admitted he had had a sleepless night, reported the Yonhap News agency.

"I guess the attention of all our people must currently be directed toward Singapore," he said, after watching the live broadcast of the opening of the meeting.

Mr Moon and his Cabinet delayed their weekly meeting for more than 10 minutes to watch the historic handshake.

"I too spent a sleepless night. I, along with all our people, sincerely hope that it will be a successful summit that will open a new era of complete denuclearisation, peace and a new relationship between South Korea, North Korea and the United States," Moon said, according to presidential office pool reports.

Earlier this week, Moon attempted to manage expectations for the unprecedented meeting.

He stressed that the success of the U.S.-North Korea summit would only be the start of a "long process" to completely denuclearise the North and establish lasting peace between North and South, two countries technically at war since the Korean War of 1950-53 ended with an armistice and not a peace treaty.

"The deep-rooted hostile relationship and the North Korean nuclear issue cannot be resolved in one single action in a meeting between leaders," Moon told his top aides on Monday.

"Even after the two leaders open the dialogue, we will need a long process that may take one year, two years or even longer to completely resolve the issues."

Although South Korea does not have a seat at the table today, the South Korean public are waiting eagerly to hear the outcome.

Trending words on South Korean social media right now include "peace declaration", "meeting of the century", "The North Korean flag and star spangled banner"

03:55AM 'Like a science fiction movie'

CNN's Jim Acosta says Kim Jong-un was caught on tape remarking that this was like "a science fiction movie".

U.S. President Donald Trump, right, and North Korean leader Kim Jong Un walk together during their official meetings credit: AP

03:51AM The meeting - in pictures

Some more remarkable pictures are emerging from the summit. And just to remind you, all this is happening about 220 miles from where Kim Jong-un's half brother Kim Jong-nam was assassinated - allegedly at the behest of the North Korean leader.

North Korean leader Kim Jong-un and Donald Trump share a joke as they shake hands during their historic summit credit: Getty

North Korea leader Kim Jong Un and U. S. President Donald Trump stand together at the Capella resort on Sentosa Island credit: AP

03:33AM Rodman: 'Obama didn't even give me the time of day'

Rob Crilly has filed on Dennis Rodman's unusual appearance on CNN.

The former basketball star broke down on live television as he described his feelings of vindication at the historic meeting between Donald Trump and Kim Jong-un.

Read the full story here.

His appearance also raised eyebrows among some North Korea experts.

03:25AM Snap analysis

The Telegraph's Tim Stanley gives his initial verdict on what we've seen so far.

03:16AM Who's at the table

The two delegations are now getting down to the serious business of resolving the problem of Kim Jong-un’s nuclear weapons, writes Nicola Smith in Singapore.

Four men from each delegation are currently sitting on opposite sides of an imposing polished wooden table.

In Team Trump, we have Mike Pompeo, the secretary of state, John Bolton, the national security advisor and John Kelly, the White House chief of staff.

U.S. President Donald Trump shakes hands with North Korea's leader Kim Jong Un before their expanded bilateral meeting in Singapore credit: Reuters

Team Kim includes Ri Su Yong, a top foreign affairs official, Kim Yong Chol, the former spy chief, and Ri Yong Ho the foreign minister. No sign of Kim’s younger sister, Kim Yo-jong, who sat next to him during his talks with Moon Jae-in, the South Korean president in April.

The female interpreter is also in the room.

03:12AM 'We will solve it'

After the meeting with Kim Jong-un, Mr Trump said that by "working together, we will get it taken care of".

"We will solve it," he added ahead of the expanded bilateral meeting.

U.S. President Donald Trump is seen with North Korea's leader Kim Jong Un before their expanded bilateral meeting in Singapore credit: Reuters

03:07AM The anatomy of a leader

So great has been the scrutiny of this summit, one South Korean paper has apparently analysed the body of Kim Jong-un.

03:00AM One-to-one meeting has ended

The two leaders have finished their one-to-one, with the US president saying it was "very, very good". He added that they have an "excellent relationship".

John Kelly, Mike Pompeo and John Bolton will now join them for an expanded bilateral meeting.

US President Donald Trump gives a thumbs up as he sits down with North Korea's leader Kim Jong-un credit: AFP

02:42AM Dennis Rodman gets emotional on CNN

The former basketball star got tearful as he spoke on CNN about his meetings with Kim Jong-un.

02:38AM The meeting - in pictures

U.S. President Donald Trump and North Korean leader Kim Jong Un prepare to shake hands at the Capella Hotel on Sentosa island in Singapore credit: Reuters

Donald Trump prepares to shake hands with Kim Jong-un credit: Reuters

The handshake itself credit: AFP

Donald Trump pats the arm of Kim Jong-un after shaking his hand credit: AFP

02:32AM "Long, firm and historic'

The Telegraph's Tim Stanley is in Singapore and has this on the handshake.

Donald Trump and Kim Jong-un’s handshake was long, firm and historic. Mr Trump arrived at the Capella hotel on Sentosa island looking slightly pensive, fiddling with his jacket buttons; Mr Kim appeared relaxed. When they met – striding towards each other in front of a row of DPRK and USA flags – one was one struck immediately by the height difference. Mr Trump, towering above the North Korean, patted him on the back, asserting dominance in the way Western politicians and businessmen have been trained to do. The handshake – that astonishing, ground-breaking handshake – lasted about 10 seconds. There was a fierce debate among my fellow reporters over which hands were bigger.

U.S. President Donald Trump shakes hands with North Korean leader Kim Jong Un at the Capella Hotel on Sentosa island in Singapore credit: Reuters

Next came the sit down for the cameras. Mr Kim, leaning forward and smiling now, said it was “not easy to get here” and spoke of “overcoming” old prejudices. Mr Trump – legs spread apart, fingers forming a triangle – said he agreed and reached out to offer another handshake. They clearly wanted to get down to business. This meeting represents a radical change in decades of policy, and yet it also seemed quite normal, even unpretentious. What comes of it we shall hopefully find out later.

02:18AM Trump expects 'great relationship' with Kim

The pair gave a few comments before beginning talks.

Mr Trump predicts he will have a "great relationship" with Kim Jong-un and expects the summit will be a great success.

Mr Kim said they had overcome "all obstacles" to hold this summit. They then shook hands for a third time.

02:07AM The moment

02:06AM Trump and Kim greet each other

Donald Trump and Kim Jong-un have met and shaken hands ahead of their summit.

Mr Trump, who is 6 foot 3 inches, towered over Kim, who is around 5 foot 7 inches and close to 40 years younger than the US president.

02:02AM And we're set

02:00AM More on Kudlow

Larry Kudlow, the chief White House economic adviser, suffered a heart attack and is being treated at a Washington area hospital, according to a tweet sent from President Donald Trump's Twitter account.

Larry Kudlow credit: Bloomberg

Mr Kudlow made headlines after the G7 summit when he appeared on Sunday morning talks shows to deliver a blistering attack on Justin Trudeau, the Canadian prime minister.

Click here to read more.

01:58AM Boost for North Korea

01:47AM The scene is set

01:41AM Trump tweets that aide has suffered heart attack

The US president has tweeted some news from the US, saying his chief economic adviser has suffered a heart attack.

01:38AM Kim arrives

And now Kim Jong-un has arrived at the Capella Hotel.

The motorcade of North Korea leader Kim Jong Un leaves the St. Regis Hotel on the way to the Capella Hotel credit: AP

We're about 20 minutes away from that historic handshake - a moment that Trump is known to use as a diplomatic power play.

01:25AM Trump arrives

Mt Trump has arrived at the summit site on Singapore's Sentosa Island for the historic meeting,

Kim Jong-un will be joining him shortly.

01:22AM Kim Jong-un’s remarkable turnaround

Ben Riley-Smith, US editor, has this from Singapore:

Just for a moment, let us dwell on quite how remarkable this meeting between Kim Jong-un and Donald Trump really is today.

Last year, Kim was an international outcast. He was testing nuclear weapons with the hope of developing one that could hit mainland America.

The brutal assassination of his half-brother Kim Jong-nam, murdered with a nerve agent in early 2017, was likely at the behest of Kim himself.

View more!

His regime had dubbed Mr Trump a “mentally deranged US dotard" - someone who is senile - and was in turn called “Little Rocket Man” by the US president.

The North Korean regime was the target of some of the hardest-hitting economic sanctions ever passed by the United Nations while Mr Trump’s administration was debating the merits of a military attack.

And yet, in 35 minutes, Mr Trump will meet alone with Kim, save for translators. No sitting US and North Korea leaders have ever met before.

Whether the talks will bring the breakthrough on denuclearisation that the Trump administration hopes is not at all clear.

North Korea's leader Kim Jong Un, accompanied by Singapore's Foreign Minister Vivian Balakrishnan, visits Singapore credit: Reuters

US media reports have suggested North Korean officials have pushed back on the demand and experts are suspicious of Kim’s Damascene conversion to peace.

But Kim has already won one achievement - recognition.

He has met the leaders of China and South Korea twice each this year, and imminently the US leader too. The heads of Russia, Japan and even Syria could be next.

An international pariah just six months ago, the North Korean leader is now meeting the world’s most powerful men. That will likely continue, whatever happens today.

01:16AM Kim Jong-un leaves for summit

And now the North Korean leader has left his hotel, the St Regis, and his headed to the summit venue. There is about 45 minutes to go before it is due to start.

01:12AM Trump tweeting in the car

Trump locked in and focused. Tweeting about domestic victories as he goes.

01:09AM So what might happen today?

Professor Robert Kelly, (yes, that one), has outlined succinctly the possible outcomes today.

"So I figure this thing today will go 1 of two ways. 1. Team Trump really does have almost nothing out of the N Koreans. The scramble yesterday was an effort to get something, anything out of them, including conceding extraordinary security guarantees. This is why success has been repeatedly re-defined downward from a Nobel a month to just more talks in the future today. This is also why the whole thing has been chopped to a short event. They just don’t have much. The other possibility is that some kind of deal has been worked out, and it will be sprung upon us for the surprise theatrics Trump loves so much. This would of explain Pompeii’s confidence yesterday about ‘rapid progress,’ in which case the summit’s been chopped down, because the extra time is not needed.

01:05AM Trump departs for summit

Mr Trump has left the Shangri-La Hotel and is heading for the summit venue at the Capella hotel on the island of Sentosa.

12:42AM Who are the negotiators?

Here's a quick who's who of who will be facing off in the room today.

View more!

Read more here about the small army of diplomats, experts and officials who have been working tirelessly behind the scenes in the run-up to the historic summit to ensure it goes without a hitch.

12:25AM Trump to do interview after summit

Fox News says the US President will sit down with host Sean Hannity shortly after the summit.

The broadcaster says the interview will take place at the Capella Hotel on Sentosa Island in Singapore before the US president departs the city state in the evening.

The interview will air on Fox's "Hannity" at 9 pm on Tuesday in the US - 2am BST.

Fox News says Trump will talk about the meeting with Kim and future relations between the two countries.

Hannity is a friend and confidant of the president and speaks out in support of Trump on his show.

12:16AM US officials on the move

Mike Pompeo, the US Secretary of State, says on Twitter the US side is "ready for today" as he posted a picture of the US delegates apparently preparing to to head off.

12:12AM North Korean media on Kim's walkabout

North Korean state media described Kim Jong-un’s walkabout in Singapore on Monday night as a tour to learn about “social and economic development.”

The Korean Central News Agency (KCNA) made a rare disclosure of the young leader’s whereabouts, confirming that he had toured some of Singapore’s most famous sites.

Kim was seen on international news broadcasts smiling and waving to astonished crowds, as he walked through some of the city-state’s business night entertainment spots, and took in the panorama of Singapore’s business district from the rooftop of the exclusive Marina Bay Sands hotel.

At the start of the excursion, Vivian Balakrishnan, posted a selfie with Kim on Twitter, with the teasing hashtag, #guesswhere?

KCNA opted for a more sober tone.

"Going round the Great Flower Garden, one of the prides of Singapore, Sky Park located on the roof of the world-famous Marina Bay Sands building and Singapore Port, he learned about the social and economic development of the Republic of Singapore," it said.

12:00AM Plan for the day

Here's the planned running order of the day.

9am local [2am BST]: Trump meets Kim. One-on-one meeting (plus translators) begins 9.15 and due to last 45 minutes

10am: Pompeo (secretary of state), John Kelly, chief of staff, and John Bolton, National Security Adviser join a bilateral meeting

11:30am: Meeting is further expanded with team including Sarah Sanders, White House press secretary, and Sung Kim, key negotiator, joining for a working lunch

4pm: Trump press conference.

7pm: Trump leaves for Washington

11:36PM Kim the tourist

Kim Jong-un has rarely left his country as leader, so the North Korean leader has taken the chance to do some sight-seeing in Singapore.. He even posed for what is thought to be his first "selfie".

The North Korean dictator smiled as Vivian Balakrishnan, the city-state's foreign minister, took a photograph of them together on his mobile phone, which he then posted on Facebook and Twitter, writes Nick Allen.

Ong Ye Kung, Singapore's education minister, also squeezed into the historic selfie, his shoulder touching Kim's.

Read the full story.

11:21PM Trump kicks off the day with tweets

With less than three hours to go until the summit, the US president has started this historic day in customary fashion - on Twitter.

He was his usual combative self, taking a swipe at past presidents' efforts to tackle North Korea as well as those critical of his current efforts.