The unprecedented encounter in Singapore Tuesday 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.

In its first report on the landmark summit, the official KCNA news agency ran a glowing dispatch on the talks, describing them as an "epoch-making meeting" that would help foster "a radical switchover in the most hostile (North Korea)-US relations".

The report said the two men each asked the other to visit their country.

"The two top leaders gladly accepted each other's invitation," KCNA said.

Pyongyang has reason to feel confident after the meeting which was a major coup for an isolated and heavily sanctioned regime that has long craved international legitimacy.

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.

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.

The KCNA report said Trump committed to ending the drills during his meeting with Kim. 

It added that denuclearisation on the Korean peninsula would be dependent on the two sides "refraining from antagonising... each other out of mutual understanding".

- Smiles and handshakes -

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.

World powers from China to Japan, the European Union and Russia welcomed its outcome -- while cautioning it was only the first step towards resolving the nuclear stand-off with Pyongyang.

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, critics charged, feting a regime which stands accused of widespread human rights abuses.

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 Kim, whom he described as "very talented".

KCNA said the two leaders ate and walked together, "deepening friendly feelings" towards each other.

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.

Speaking later as he flew out of Singapore bound for the US territory of Guam -- towards which Pyongyang last year threatened to lob missiles -- Trump said he intended to hold North Korea to its word on denuclearisation.

"We're going to have to check it and we will check it. We'll check it very strongly," he told reporters on Air Force One.