The extraordinary and unprecedented encounter in Singapore saw the leader of the world's most powerful democracy shake hands with the third generation scion of a dynastic dictatorship, standing as equals in front of their nations' flags.

Kim agreed to the "complete denuclearisation of the Korean Peninsula", a stock phrase favoured by Pyongyang that stopped short of long-standing US demands for North Korea to give up its atomic arsenal in a "verifiable" and "irreversible" way.

And in a blockbusting press conference after the summit, Trump said the US would halt military exercises with Seoul -- something long sought by Pyongyang, which claims the drills are a rehearsal for invasion.

With Pyongyang having declared a moratorium on weapons testing on the grounds its development programmes were complete, the move looked like a tacit acceptance of the "freeze for freeze" proposal pushed by Beijing and previously decried by Washington.

The US stations around 30,000 troops in security ally South Korea to protect it from its neighbour, which invaded in 1950 in an attempt to reunify the peninsula by force.

"We will be stopping the war games which will save us a tremendous amount of money," Trump told reporters, adding that "at some point" he wanted to withdraw US troops from the South.

Both Seoul and US military commanders in the South indicated they had no idea the announcement was coming, and analysts expressed immediate concern.

Ending the drills "is in excess of all expert consensus, South Korean requests, and even a close reading of North Korean demands", said Adam Mount of the Federation of American Scientists.

- All smiles -

The Singapore summit was 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, and ahead of the meeting, critics expressed concerns that it risked being more about headlines than substantive progress.

It also legitimised Kim, whose regime stands accused of widespread human rights abuses, critics charged.

In the event, the two leaders showered each other with compliments in the sumptuous setting of a luxury Singapore hotel, a marked contrast from their previous rounds of mutual insults, such as "mentally deranged" and "little rocket man".

Trump said he had formed a "special bond" with the "very talented" Kim, who is suspected of ordering the assassination of his brother at a Malaysian airport last year.

After a day filled with smiles and handshakes watched around the world, the US "committed to provide security guarantees" to North Korea, while Pyongyang committed to "work towards" denuclearising the Korean peninsula.

Melissa Hanham of the US-based Center for Nonproliferation Studies said on Twitter that North Korea had "already promised to do this many times," adding the two sides "still don't agree on what 'denuclearisation' means."

Asked about the issue -- the crux of the summit -- Trump said "we're starting that process" which would begin "very, very quickly", but gave no concrete details.

US sanctions would remain in place until Washington had seen progress, he added, before flying out of Singapore bound for the US territory of Guam -- towards which Pyongyang had last year threatened to lob missiles.

- We'll meet again -

"We'll meet again," Trump said after the signing ceremony, standing with Kim on the verandah where they first met. "We will meet many times."

He "absolutely" would be willing to invite Kim to the White House, and would do so when the time was right, he added.

For his part, Kim -- who made headlines the evening before the summit with an nighttime visit to major tourist sites -- said the two Cold War foes had vowed to "leave the past behind", pledging "the world will see a major change".

Abraham Denmark of the Wilson Center in Washington tweeted: "It seems Kim got a huge propaganda win and a metric ton of legitimacy, and the US gave up joint exercises, for little new and nothing in return."

But he added: "The silver lining is that dialogue will continue, and where there is diplomacy there is hope."