US President Donald Trump has said he had walked away from a nuclear deal at his summit with Kim Jong-un because of unacceptable demands from the North Korean leader to lift punishing US-led sanctions.

Mr Trump said two days of talks in the Vietnamese capital, Hanoi, had made good progress in building relations and on the key issue of denuclearisation, but it was important not to rush into a bad deal.

"It was all about the sanctions," Mr Trump said at a news conference after the talks were cut short.

"Basically, they wanted the sanctions lifted in their entirety, and we couldn't do that."

The United Nations and the United States ratcheted up sanctions on North Korea when the reclusive state undertook a series of nuclear and ballistic missile tests in 2017, cutting off its main sources hard cash.

Both Mr Trump and Mr Kim left the venue of their talks, the French-colonial-era Metropole hotel, without attending a planned lunch together.

"Sometimes you have to walk, and this was just one of those times," Mr Trump said, adding "it was a friendly walk". He later left Vietnam to return to Washington.

Failure to reach an agreement marks a setback for Mr Trump, a self-styled dealmaker under pressure at home over his ties to Russia and testimony from Michael Cohen, his former personal lawyer who accused him of breaking the law while in office.

Mr Trump said Cohen "lied a lot" during Congressional testimony in Washington yesterday, though he had told the truth when he said there had been "no collusion" with Russia.

The collapse of the talks will likely raise questions about the Trump administration's preparations and about what some critics see as his cavalier style of personal diplomacy.

Since their first summit in Singapore in June, Mr Trump has stressed his good chemistry with Mr Kim, but there have been questions about whether the bonhomie could move them beyond summit pageantry to substantive progress on eliminating a North Korean nuclear arsenal that threatens the United States.

"No deal is a surprise, especially as they were both all smiley last evening," said Lim Soo-ho, senior research fellow at the Institute for National Security Strategy.

"But no-deal today doesn't mean there won't be one in coming months. It means stakes were way too high for the two leaders to give another wishy-washy statement like they did in Singapore."

The Singapore summit, the first between a sitting US president and a North Korean leader, produced a vague statement in which Mr Kim pledged to work toward denuclearisation of the Korean peninsula.

But little progress followed.

News of the summit failure sent South Korea's currency lower and knocked regional stock markets. South Korea's Kospi index closed 1.8% lower, marking the biggest one-day percentage loss since October 2018.

North Korea's old rival South Korea, which backs efforts to end confrontation on the peninsula, said it regretted that no deal had been reached but the two sides had made progress.

While Mr Trump had said he was in no rush to strike a deal with North Korea, the White House had been confident enough tos chedule a "joint agreement signing ceremony" at the conclusion of talks. Like the lunch, the ceremony did not take the place.

There was no indication of when Mr Trump and Mr Kim might meet again but the White House said the "respective teams look forward to meeting in the future".

Kicking off their second day in Hanoi, Mr Trump said he would be happy as long as North Korea conducted no more nuclear or intercontinental ballistic missile tests.

North Korea has conducted no nuclear or intercontinental ballistic missile tests since late 2017, and Mr Trump said Mr Kim had promised him there would be no more.

Mr Trump said he and Mr Kim had discussed dismantling North Korea's main nuclear facility at Yongbyon, which Mr Kim was willing to do, but he had wanted sanctions relief first.

There were other facilities that Mr Trump said he had raised, and the North Koreans had been surprised the Americans knew about them, but they had not been able to agree on them.

"We asked him to do more and he was unprepared to do that, but I'm still optimistic," US Secretary of State Mike Pompeo told the news conference, referring to Mr Kim.

Mr Trump said the US would be able to inspect some North Korean facilities but he did not go into specifics.