DONALD Trump has insisted he "had to walk" from his summit with Kim Jong-un after the pair failed to agree a nuke deal and their lunch was dramatically cancelled.

The leaders scrapped a planned signing ceremony as their second day of crunch talks in Hanoi, Vietnam, ended without an agreement on how to denuclearise the Korean peninsula.

At a press conference, the US President said the despot refused to dismantle North Korea's Yongbyon nuclear complex and wanted the sanctions imposed on his crackpot regime lifted.

While insisting the two leaders had spent some "productive time" together, Trump said: "Sometimes you have to walk."

The US President continued: "They wanted the sanctions lifted. And we were unwilling to do that.

"We will end being very good friends with chairman Kim and North Korea. They have amazing potential.

"He has a certain vision. Itís not exactly our vision. But itís a lot closer than we were a year ago."

The brash New Yorker said that the North Korea leader wants to "denuke a portion" of his country - which was another point of contention for the US administration.

He added that Kim promised that he would not resume testing of ballistic missiles despite the talks breaking down.

On his relationship with murderous dictator Kim, Trump said: "We spent pretty much all day with Kim Jong-un.

"He is quite a guy, quite a character. I think our relationship is strong."

He later added: "We like each other, (we have a) good relationship."

US Secretary of State Mike Pompeo also spoke about the failed summit, saying: "We made real progress. We didnít get all the way.

"We didnít agree on something which would make sense for the United States of America."

Earlier, White House press secretary Sarah Sanders says the two leaders discussed denuclearization of the Korean Peninsula.

She adds: "No agreement was reached at this time, but their respective teams look forward to meeting in the future."

Still, Sanders is describing the meetings between Trump and Kim as "very good and constructive."

Trump and Kim departed the hotel where they've been holding summit negotiations far earlier than planned Thursday.

A joint agreement signing ceremony was scrapped.

It comes after President Trump insisted there was "no rush" on forging a lasting agreement - adding: "We just want to do the right deal".

They were joined by US Secretary of State Mike Pompeo and North Korean official Kim Yong Chol.

The chumminess between Chairman Kim and Trump marks a stark contrast to a year ago - when the US President threatened to rain "fire and fury" in Pyongyang over its nuke tests.

Mr Trump said on Thursday: "The relationship is just very strong and when you have a good relationship a lot of good things happen."

He added that "a lot of great ideas were being thrown about" at their lavish dinner the previous night - but did not offer specifics.

Cheerful Kim, speaking through a translator, added: "I believe by intuition that good results will be produced."

The 35-year-old reclusive leader said: "I believe that starting from yesterday, the whole world is looking at this spot right now.

"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."

Possible outcomes could include a peace declaration for the Korean War that the North could use to eventually push for the reduction of US troops in South Korea.

The North also desperately wants sanctions relief that could allow Pyongyang to pursue lucrative economic projects with the South.

But sceptics say such agreements would likely leave in place a significant portion of North Korea's nuclear-tipped missiles - while robbing the United States of its negotiating leverage.

Asked if this summit would yield a political declaration to end the Korean War, Trump told reporters on Wednesday: "We'll see."

The President's schedule Thursday promised a "joint agreement signing ceremony" after the meeting.

The leaders' first face-to-face in June was heavy with historic pageantry but light on any enforceable agreements for North Korea to give up its nuclear arsenal.

But the latest meeting comes against a backdrop of tumult and investigations at home for President Trump.

Hours before he sat down again with Kim, Trump's former personal attorney Michael Cohen delivered explosive congressional testimony claiming the president is a "conman" who lied about his business interests with Russia.

Trump last night tweeted that Cohen "did bad things unrelated to Trump" and "is lying in order to reduce his prison time."

Cohen has been sentenced to three years in prison for lying to Congress.

After their first summit, where Trump and Kim signed a joint statement agreeing to work toward a denuclearized Korean Peninsula, the president prematurely declared victory.

He tweeted that "There is no longer a Nuclear Threat from North Korea" - but this has still not been proven.

North Korea has spent decades building its nuclear program - and there are doubts that it will give away that program without getting something substantial in return.

The Korean conflict ended in 1953 with an armistice - essentially a cease-fire signed by North Korea, China and the 17-nation, U.S.-led United Nations Command.