Donald Trump has formed a "special bond" with North Korea's leader Kim Jong-un, he said Tuesday at the end of a historic meeting during which the two former foes pledged to meet again.

The pair signed what Trump called a "pretty comprehensive" and "very important" document, which spoke of "new US-DPRK relations" and committed Washington to "security guarantees".

However, asked about denuclearisation -- the crux of the summit, Trump said "we're starting that process", adding that it would begin "very, very quickly."

 

- 'Fire and fury' -

Some analysts have warned the summit could produce more style than substance and Kelly Magsamen, a former top Pentagon Asia specialist, said:

"We'll see if Kim actually gives him anything more than superficial pleasantries and some good TV."

Critics said the mere fact of the meeting meant Trump was legitimising Kim, who critics say runs a police state where human rights are routinely trampled.

"It's a huge win for Kim Jong-un, who now -- if nothing else -- has the prestige and propaganda coup of meeting one-on-one with the president, while armed with a nuclear deterrent," said Michael Kovrig, Crisis Group Senior Adviser for North East Asia.

The warm words and positive optics seemed a different era from when Trump was threatening to rain down "fire and fury" on Pyongyang and Kim attacked Trump as a "mentally deranged US dotard", as he fired off a series of provocative weapons tests.

The Singapore summit is a potentially legacy-defining meeting for both men -- comparable to president Richard Nixon's 1972 visit to China, or Ronald Reagan's 1986 summit with Mikhail Gorbachev in Reykjavik.

But many agreements have been made in the past with North Korea that have later fallen apart.

On the table is the vexed question of denuclearisation -- a word that means vastly different things to the two parties.

It remains far from clear that Pyongyang is willing to give up its nukes -- weapons that the regime sees as its ultimate guarantee of survival.

And on the eve of the meeting, aides for both men were still scrambling to narrow yawning differences.

Secretary of State Mike Pompeo said Monday that the United States was willing to offer Pyongyang "unique" security guarantees if it denuclearises.

But the summit was more likely it is the start of a longer process of negotiation.

The discussions "will set the framework for the hard work that will follow", Pompeo said. (AFP)