Trump and North Korean leader Kim Jong-un issued a joint statement after their historic meeting in Singapore on Tuesday that reaffirmed the North's commitment to "work toward complete denuclearisation of the Korean Peninsula" and gave US guarantees of security to North Korea.

Democratic critics in the US say the agreement was short on detail and the Republican president had made too many concessions to Kim, whose country is under UN sanctions for its nuclear and weapons programs and is widely condemned for human rights abuses.

North Korea's state media hailed the summit as a success, including highlighting Trump's surprise announcement after the meeting that the US would stop military exercises with South Korea, which the North has long sought.

Despite the lack of detail in the summit agreement, Trump stressed at a news conference afterward that he trusted Kim to follow through.

He returned to Washington on Wednesday and hailed the meeting, the first between a sitting US president and a North Korean leader, as a major win for American security.

"Everybody can now feel much safer than the day I took office," Trump tweeted.

"There is no longer a nuclear threat from North Korea. Meeting with Kim Jong Un was an interesting and very positive experience. North Korea has great potential for the future!"

Kim has also returned home, the North's official news agency said, amid speculation Kim stopped by in Beijing to brief Chinese President Xi Jinping on the outcome of the summit.

Secretary of State Mike Pompeo, who is charged by Trump with leading follow-on negotiations, said the US hopes to achieve "major disarmament" by North Korea within the next 2-1/2 years.

"One trip and it's 'mission accomplished,' Mr. President? North Korea still has all its nuclear missiles, and we only got a vague promise of future denuclearisation from a regime that can't be trusted," said Adam Schiff, the top Democrat on the US House of Representatives Intelligence Committee.

"North Korea is a real and present threat. So is a dangerously naive president," he wrote on Twitter.

Senator Chris Van Hollen, also a Democrat, said of Trump's tweet about North Korea no longer presenting a threat: "This is truly delusional."

The summit statement provided no details on when Pyongyang would give up a nuclear weapons program or how the dismantling might be verified.

Sceptics of how much the meeting achieved pointed to the North Korean leadership's long-held view that nuclear weapons are a bulwark against what it fears are US plans to overthrow it and unite the Korean Peninsula.

The US has long insisted on complete, verifiable and irreversible denuclearisation by North Korea, but in the summit statement, North Korea committed only to the "complete denuclearisation of the Korean Peninsula," phrasing it has used in the past.

Pompeo bristled at a question about why the words "verifiable" and "irreversible" were not in the summit joint statement, in the context of denuclearisation.

"It's in the statement. You're just wrong about that ... Because complete encompasses verifiable and irreversible. I suppose you could argue semantics, but let me assure you that it's in the document," Pompeo said.

Australian Associated Press