Kim Jong-un has pledged his “firm and unwavering commitment to the complete denuclearisation of the Korean peninsula” following a historic meeting with Donald Trump.

The US “committed to provide security guarantees” to North Korea, according to an agreement signed by both leaders in Singapore following decades of hostilities between the two nations.

Mr Trump said he expected the denuclearisation process to start “very, very quickly”. US secretary of state Mike Pompeo and North Korean officials will hold follow-up negotiations “at the earliest possible date”, the joint statement said.

However, the document did not give a definition of denuclearisation or details of how it would be achieved.

It also also made no mention of the crippling international sanctions imposed on North Korea as it pursued its nuclear weapons programme.

Nor was there any reference to the signing of a peace treaty. The US and North Korea technically remain in a state of warfare as the 1950-53 Korean War, in which millions of people died, was concluded only with a truce.

But the joint statement did say the two sides had agreed to the recovery and repatriation of the remains of prisoners of war and those missing in action.

If the agreement leads to a lasting easing of hostilities, it could fundamentally change the security landscape of north-east Asia, just as former US president Richard Nixon visit to Beijing in 1972 led to the transformation of China.

Donald Trump holds up a document signed by him and North Korea’s leader Kim Jong-un (AFP/Getty Images)

Before signing what Mr Trump described as a “comprehensive” document, Mr Kim said the two leaders had a historic meeting “and decided to leave the past behind”.

“The world will see a major change,” the North Korean leader added.

The joint statement contained four bullet-pointed commitments, one of which stressed “efforts to stablish new relations in accordance with the desire of the peoples of the two countries for peace and prosperity”.

The US and North Korea will also “join their efforts to build a lasting and stable peace regime on the Korean Peninsula”, the agreement stated.

The White House has yet to release the document’s text, but it was photographed by the media as Mr Trump displayed it at a signing ceremony at the resort island of Sentosa.

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

During an after-lunch stroll through the gardens of the hotel where the summit was held, Mr Trump said the meeting had gone “better than anybody could have expected”.

Mr Kim stood silently alongside, but the North Korean leader had earlier described the meeting as a “a good prelude to peace”.

The president said he had formed a “very special bond” with Mr Kim and that the US relationship with North Korea would be very different.

“People are going to be very impressed and people are going to be very happy and we are going to take care of a very dangerous problem for the world,” Mr Trump said

He described Mr Kim “very smart” and a “very worthy, very hard negotiator.”

“I learned he’s a very talented man. I also learned that he loves his country very much,” he added.

US-North Korea agreement The four commitments signed by Donald Trump and Kim Jong-un 1. The United States and the DPRK commit to establish new US-DPRK relations in accordance with the desire of the peoples of the two countries for peace and prosperity. 2. The United States and the DPRK will join their efforts to build a lasting and stable peace regime on the Korean Peninsula. 3. Reaffirming the April 27, 2018 Panmunjom Declaration, the DPRK commits to work towards the complete denuclearisation of the Korean Peninsula. 4. The United States and the DPRK commit to recovering POW/MIA remains, including the immediate repatriation of those already identified.

Mr Trump had predicted on Saturday he would be know within a minute of meeting the North Korean leader whether they would reach a deal.

They had appeared cautious and serious when they first arrived for the summit at the Capella hotel on Sentosa, a resort with luxury hotels, a casino, manmade beaches and a Universal Studios theme park.

But, with cameras of the world’s media trained on them, they displayed an initial atmosphere of bonhomie as they met on the hotel’s verandah of the hotel, a refurbished 19th century British regimental officers’ mess.

Body language expert said both men tried to project command as they met, but also displayed signs of nerves.

After a handshake, the leaders were soon smiling and holding each other by the arm, before Mr Trump guided Mr Kim to the library where they held a meeting with only their interpreters.

Inside, they sat alongside each other against a backdrop of North Korean and US flags, Mr Kim beaming broadly as the president gave him a thumbs up.

After initial exchanges lasting around 40 minutes, the leaders emerged, walking side-by-side through the hotel before entering a meeting room where they were joined by their most senior officials.

Mr Trump was joined by Mr Pompeo, as well as national security adviser John Bolton, and John Kelly, White House chief of staff, for the expanded talks. Mr Kim’s team included former military intelligence chief Kim Yong-chol, foreign minister Ri Yong-ho and Ri Su-yong, vice-chairman of the ruling Workers’ Party.

In the hours before the summit began, Mr Trump expressed optimism while Mr Pompeo injected a note of caution about whether Mr Kim would prove to be sincere about his willingness to denuclearise.

The secretary of state said the meeting should set the framework for “the hard work that will follow”, insisting that North Korea had to move towards complete, verifiable and irreversible denuclearisation.

Pyongyang, however, has shown little appetite for surrendering nuclear weapons it considers vital to the survival of Mr Kim’s dynastic rule.

Sanctions on North Korea would remain in place until that happened, Mr Pompeo said on Monday.

“If diplomacy does not move in the right direction... those measures will increase,” he added.

The White House said later that discussions with North Korea had moved “more quickly than expected” and Mr Trump would leave Singapore on Tuesday night following the summit, rather than Wednesday, as previously scheduled.

Mr Kim was due to leave on Tuesday afternoon, said a source involved in planning his visit .

Mr Trump spoke to South Korean president Moon Jae-in and Japan’s prime minister Shinzo Abe, both key allies of Washington in the region, to discuss developments ahead of the summit.