Donald Trump and Kim Jong-un shake hands in Singapore

Donald Trump appears to have made a major concession to North Korea following his joint agreement with Kim Jong-un, ending joint military exercises with South Korea that he deemed “provocative” and “tremendously expensive”.

He said he also hoped to “bring home” the 32,000 US troops stationed in South Korea at some point in the future, but acknowledged such a move was not “part of the equation right now”.

In a press conference lasting more than an hour Mr Trump also said the North had begun dismantling a major missile engine testing site, and he praised Mr Kim as “very talented”.

Later, as Mr Trump's plane landed in Guam to refuel, Mr Trump told reporters that he trusted Mr Kim and that he believed the North Korean leader was sincere about his desire for denuclearisation.

“I can only tell you that from the time I’ve (dealt) with him, which is really starting 90 days ago," Mr Trump said. "I think he wants to get it done".

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At the end of the summitMr Trump and Mr Kim signed what Mr Trump claimed was a “comprehensive” document following the historic meeting aimed at the denuclearisation of the Korean peninsula. The president said he believed the process of denuclearisation would happen “very, very quickly”, adding that he had formed a “special bond” with Mr Kim.

Mr Kim who has been granted a measure of international legitimacy with the summit, said the two leaders had “decided to leave the past behind. The world will see a major change”.

In the first meeting of a sitting US president and a North Korean leader, the pair convened at a luxury resort on Singapore’s Sentosa Island, clasping hands as they stood on a red carpet in front of a backdrop of alternating US and North Korean flags. Mr Trump was first to arrive at the summit site, followed by Mr Kim, both readying for the 9am meeting that culminated dizzying weeks of negotiations over logistics and policy.

The pair started the momentous Singapore summit with an historic handshake for the world’s media before getting down to talks about North Korea’s nuclear programme.

Mr Trump and Mr Kim met one on one for about 40 minutes, joined only by translators. Then aides to each arrived for more discussions and a working lunch.

Singapore Summit: historic first meeting between Trump and Kim Jong-un Show all 20 1 /20 Singapore Summit: historic first meeting between Trump and Kim Jong-un Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Trump and Mr Kim leave following their historic meeting AFP/Getty Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Trump and Mr Kim sign a document committing to peace between their nations, amongst other things EPA Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Trump holds up a document that both he and Mr Kim have signed AFP/Getty Singapore Summit: historic first meeting between Trump and Kim Jong-un The two leaders reach out to shake hands for the first time AP Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Trump and Mr Kim shake hands as they meet for the first time Reuters Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Trump and Mr Kim walk off stage, following their historic meeting Reuters Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Trump and Mr Kim take a stroll after their meeting on June 12 Reuters Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Trump and Mr Kim interrupt their stroll to talk to the media AP Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Kim and Mr Trump look out over a balcony at the Capella hotel, where they held their meeting on June 12 Reuters Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Trump takes questions at the press conference following his meeting with with Mr Kim AP Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Trump appreciates the crowd in the press conference following his meeting with Mr Kim Getty Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Trump travels to the Istana ahead of the summit with Kim Jong Un on June 12 Reuters Singapore Summit: historic first meeting between Trump and Kim Jong-un Kim Jong Un travels to the Istana ahead of the summit with President Trump on June 12 Reuters Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Kim poses for a photo with Singapore's Finance Minister Vivian Balkrishnan and Education Minister Ong Ye Kung ahead of the summit with Mr Trump Twitter/Reuters Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Trump shakes hands with Singapore Prime Minister Lee Hsien Loong, meeting on Monday June 11 in the Istana, Singapore's presidential palace AP Singapore Summit: historic first meeting between Trump and Kim Jong-un At a working lunch on Monday, Singapore's Prime Minister surprised Mr Trump with a birthday cake, in early celebration of his 72nd birthday later in the week EPA Singapore Summit: historic first meeting between Trump and Kim Jong-un US Secretary of State Mike Pompeo answers questions about the summit at a press briefing in Singapore on Monday, June 11 Getty Singapore Summit: historic first meeting between Trump and Kim Jong-un US President Donald Trump arrives at the Paya Lebar Air Base in Singapore on June 10, two days prior to his summit with North Korean leader Kim Jong Un Reuters Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Trump and Mr Kim met on Tuesday June 12 in the Capella hotel on the island resort of Sentosa, just off the south coast of Singapore AFP/Getty Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Trump boards Air Force One following the summit AFP/Getty

The US president said the meetings went “better than anybody could have expected” after the pair emerged from lunch and strolled together down a paved walkway before stopping and posing before the waiting news media.

Mr Trump said the meeting is “going great. We had a really fantastic meeting”. He added that there has been “a lot of progress. Really very positive”

It is believed that the signing will likely revolve around a promise to keep meeting.

The White House said discussions with North Korea have moved “more quickly than expected” and Mr Trump would leave Singapore on Tuesday night, after the summit. He had earlier been scheduled to leave on Wednesday. Mr Trump will visit military bases in Guam and Hawaii on his way back to Washington.

Teams of officials from both sides held working-level talks on Monday.

Senior officials travelling with Mr Trump included secretary of state Mike Pompeo, national security adviser John Bolton and White House chief of staff John Kelly. As Mr Trump was travelling to the Capella Hotel which was the site of the summit, he surprisingly tweeted about another senior official - economic adviser Larry Kudlow - with Mr Trump saying he had had a heart attack. The White House later said that Mr Kudlow was in a good condition in hospital having suffered a “very mild” heart attack.

Mr Kim’s delegation consisted of foreign minister Ri Yong Ho, defence minister No Kwang Chol and Kim Yong Chol, a close aide of Kim who has been instrumental in the diplomacy that culminated in Tuesday’s summit.

Kim Yo Jong, leader Kim’s younger sister, was also spotted in his delegation. She emerged as an influential figure in Pyongyang’s opaque leadership in February, when she led a North Korean delegation to the Winter Olympics in South Korea.

When Mr Trump initially agreed to meet with the North Korean leader, the US president spoke of his hope that their encounter could secure a major breakthrough and lead to the denuclearisation of the Korean peninsula.

If so, then the meeting would be the most important since Ronald Reagan met with Soviet leader Mikhail Gorbachev in Geneva in November 1985.

Mr Trump has since sought to play down expectations, saying that the meeting will be an important first step, but that securing a deal will likely take many more meetings.

Given that what the US wants to get out of the summit, a rapid denuclearisation of the Korean peninsula, may be different to what North Korea wants, there may be many such meetings. Many observers will be looking to see whether Mr Trump does extend an invitation to his counterpart to visit the White House.