Donald Trump said: "The relationship is just very strong and when you have a good relationship a lot of good things happen" (Picture: PA).
US President Donald Trump and North Korea's Kim Jong Un have cut short their second summit without reaching an agreement.
President Trump said North Korea wanted him to lift US sanctions in exchange for denuclearisation but he was not willing to do that, telling reporters: "Sometimes you have to walk."
But he said Mr Kim assured him he will continue to hold off on nuclear and missile tests.
White House press secretary Sarah Sanders said the leaders had a "very good and constructive meeting" and discussed ways to advance "denuclearisation and economic-driven concepts".
She said their teams "look forward to meeting in the future".
Both leaders' motorcades roared away from the central Hanoi summit site within minutes of each other after a lunch and a signing ceremony were scrapped.
In something of a role reversal, President Trump deliberately ratcheted down some of the pressure on Pyongyang, abandoning his fiery rhetoric and declaring he was in "no rush. We just want to do the right deal".
Mr Kim, asked whether he was ready to denuclearise, said:
"If I'm not willing to do that I won't be here right now."
Furthering the spirit of optimism, the leaders seemed to find a point of agreement moments later when Mr Kim was asked if the US may open a liaison office in North Korea.
Mr Trump declared it "not a bad idea" and Mr Kim called it "welcomable".
But questions persisted throughout the summit, including whether Mr Kim was willing to make valuable concessions, what President Trump would demand in the face of rising domestic turmoil and whether the meeting could yield far more concrete results than the leaders' first summit, a meeting in Singapore less than a year ago.
There had long been scepticism that Mr Kim would be willing to give away the weapons his nation had spent decades developing and Pyongyang felt ensured its survival.
President Trump had signalled a willingness to go slow, making clear he was willing to accept a more deliberate timetable for denuclearisation.
"I can't speak necessarily for today, the US President said, "but... over a period of time I know we're going to have a fantastic success with respect to Chairman Kim and North Korea."
In an unexpected development, Mr Kim on Thursday fielded questions from Western journalists for likely the first time, with the reporters receiving some coaching from the US president, who implored: "Don't raise your voice, please. This isn't like dealing with Trump."
The North Korean leader struck a largely hopeful note, saying:
"I believe by intuition that good results will be produced."
After a reporter asked Mr Kim if they were discussing human rights, President Trump interjected to say they were "discussing everything", though he did not specifically address the issue.
Earlier, accompanied only by translators, the pair displayed a familiarity with one another as they began the day's negotiations.
"The relationship is just very strong and when you have a good relationship a lot of good things happen," said Mr Trump.
He added that "a lot of great ideas were being thrown about" at their opulent dinner the night before.
"I believe that starting from yesterday, the whole world is looking at this spot right now," Mr Kim said through his translator.
"I'm sure that all of them will be watching the moment that we are sitting together side by side as if they are watching a fantasy movie."
Alison Evans, a senior research analyst at IHS Markit, told Forces News: "The US has stated that it wants not only North Korea to give up known and acknowledged sites but also other sites that North Korea has not acknowledged.
"The issue there is that obviously, North Korea is willing to talk about denuclearisation, take at least some superficial steps towards that, but North Korea has also made it clear that it is not willing to take steps that are less visible, less-understood by the public."
Possible outcomes that had been considered were a peace declaration for the Korean War that the North could use to eventually push for the reduction of US troops in South Korea, or sanctions relief that could allow Pyongyang to pursue lucrative economic projects with the South.