US president Donald Trump and North Korean leader Kim Jong Un signed a 'comprehensive' document on Tuesday following a historic summit in Singapore aimed at the denuclearisation of the Korean peninsula.

There were no immediate details on the contents of the document but Trump said he expected the denuclearisation process to start 'very, very quickly'.

Although the breakthrough made at the summit marks just the start of a diplomatic process, it could bring lasting change to the security landscape of Northeast Asia, just as former US president Richard Nixon's visit to Beijing in 1972 led to the transformation of China.

Before signing what Trump described as a 'comprehensive letter', Kim said the two leaders had a historic meeting 'and decided to leave the past behind. The world will see a major change.'

Trump said he had formed a 'very special bond' with Kim and that relationships 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,' Trump said.

Asked whether he would invite Kim to the White House, Trump said: 'Absolutely, I will.'

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

After the meetings, the two teams and other senior officials met for a working lunch, where beef short ribs, sweet and sour pork and 'Daegu Jormin', or Korean braised cod, were served for the main course, according to the menu. That was to be followed by dark chocolate tarts, pastries and vanilla ice cream for dessert. The North Korean leader's sister and close confidante Kim Yo Jong was among the lunch party.

As the cameras captured the moment, Trump quipped: 'Very nice. Getting a good picture everyone, so we all look nice and handsome and thin...perfect'.

In the hours before the summit began, Trump expressed optimism about prospects for the first-ever meeting of sitting US and North Korean leaders, while Pompeo injected a note of caution over whether Kim would prove to be sincere about his willingness to denuclearise.

Pompeo said the summit should set the framework for 'the hard work that will follow', insisting that North Korea had to move toward complete, verifiable and irreversible denuclearisation.

North Korea, however, has shown little appetite for surrendering nuclear weapons it considers vital to the survival of Kim's dynastic rule.

Sanctions on North Korea would remain in place until that happened, Pompeo said on Monday. 'If diplomacy does not move in the right direction...those measures will increase.'

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

Kim is due to leave on Tuesday afternoon, a source involved in the planning of his visit has said.

Trump spoke to Moon and Japan's prime minister Shinzo Abe, both key allies of Washington in the region, to discuss developments ahead of the summit.

'I too, got little sleep last night,' Moon told his cabinet in Seoul as the summit began in Singapore.

'I truly hope it will be a successful summit that will open a new age for the two Koreas and the United States and bring us complete denuclearisation and peace.'