US President Donald Trump said on Thursday 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.

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,' 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 Trump and 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,' Trump said, adding 'it was a friendly walk'.

Failure to reach an agreement marks a setback for 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.

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

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

Since their first summit in Singapore in June, Trump has stressed the good chemistry he has with 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 rush'

"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 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 per cent lower, marking the biggest one-day percentage loss since Oct 2018.

While Trump had said he was in no rush to strike a deal with North Korea, the White House had been confident enough to schedule 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 Trump and 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, 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.

Trump said Kim had promised him there would be no more.

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

'We asked him to some more and he was unprepared to do that,' US Secretary of State Mike Pompeo told the news conference, referring to Kim.

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

Willingness?

While Trump indicated a more flexible stance in the run-up to the Hanoi summit, critics had warned that he risked squandering vital leverage over North Korea if he gave away too much, too quickly.

U.S. intelligence officials have said there is no sign North Korea would eve give up its entire arsenal of nuclear weapons, which Kim's ruling family sees as vital to its survival.

While the United States has long demanded that North Korea give up all of its nuclear and missile programmes, the North wants to see the removal of a US nuclear umbrella for its Asian allies such as South Korea and Japan.

Earlier Kim and Trump, seated across from each other at a conference table, appeared confident of progress, and Kim had suggested he was ready to give up his nuclear bombs.

'If I'm not willing to do that, I won't be here right now,' Kim told reporters through an interpreter, when asked if he was ready to give up his nuclear weapons.

Trump, responding to that, said: 'That might be the best answer you've ever heard.'