North Korea on Friday promised further negotiations with the US, as both sides sought to hold open the door while staking out their positions after their Hanoi summit spectacularly failed to produce a nuclear deal.

The meeting between the North's leader Kim Jong Un and US President Donald Trump broke up in disarray on Thursday, with a signing ceremony cancelled and no joint communique issued.

Each sought to blame the other's intransigence for the deadlock, with Trump saying that Pyongyang wanted the lifting of all sanctions imposed on it over its banned weapons programmes.

In a rare late-night press briefing, the North's foreign minister said it had only wanted some of the measures eased, and that its offer to close "all the nuclear production facilities" at its Yongbyon complex was the best deal it could ever offer.

But the North's official KCNA news agency reported Friday that the two leaders had had a "constructive and candid exchange".

Relations between the two countries -- on opposite sides of the technically still unfinished Korean War -- had been "characterised by mistrust and antagonism" for decades, it said, and there were "inevitable hardships and difficulties" on the way to forging a new relationship.

It described the Hanoi meeting as "successful" and said Kim had promised Trump another encounter.

Similarly, Trump said before leaving the Vietnamese capital that he hoped to meet Kim again.

"Sometimes you have to walk and this was just one of those times," an unusually downbeat Trump told reporters.

"I'd much rather do it right than do it fast," he said while reaffirming his "close relationship" with Kim. "There's a warmth that we have and I hope that stays, I think it will."

The outcome in Hanoi fell far short of the pre-meeting expectations and hopes after critics said their initial historic meeting in Singapore -- which produced only a vague commitment from Kim to work "toward complete denuclearisation of the Korean peninsula" -- was more style over substance.

According to senior US officials, in the week leading up to the Hanoi summit, the North Koreans had demanded the lifting of effectively all the UN Security Council economic sanctions imposed on Pyongyang since March 2016.

Before that date, the measures were largely focused on preventing technology transfers, but more recent restrictions were imposed on several valuable industries in an effort to force concessions from Pyongyang, including coal and iron ore exports, seafood, and textile trade.

"It was basically all the sanctions except for armaments," a senior US official told reporters. "It tallies up to the tune of many, many billions of dollars."

In return they were only offering to close an "a portion of the Yongbyon complex", a sprawling site covering multiple different facilities -- and the North is believed to have other uranium enrichment plants.

Trump had urged Kim to go "all in" to secure a deal, the official said, adding Washington was willing to do so.

"The weapons themselves need to be on the table," he said, pointing to both Pyongyang's existing stock of atomic bombs and the ICBMs with which it can reach the whole of the US mainland.

But the process was continuing and Washington was "encouraged by the opportunities ahead of us", the official said. "There's still ample opportunity to talk."

Analysts say the failure to reach a deal in Hanoi does not mean the end of negotiations.

"I don't think it's a disaster and it doesn't end the dialogue process," said Chris Green of the International Crisis Group.

Trump could not afford to do "a quote-unquote 'bad deal'" in Hanoi, he added. "I think it benefits him to look tough, to string this out."

But others have pointed to a lack of preparation ahead of the meeting, with the two sides far apart and unable to bridge the gaps between them in time.

Scott Seaman of the Eurasia Group consultancy said both leaders would have to return home and rethink their strategies.

"Trump's challenge will be to dampen speculation and criticism that his unique approach is itself the problem and may well have set the US back in its efforts to end the North Korean threat," he wrote in a note.

Joel Wit and Jenny Town of the respected Washington-based 38 North project said that while there had been fears beforehand that Trump "was going to give away the store, he did just the opposite, holding out for a better deal".

"The two leaders are heavily invested in the process so hopefully, this failed summit will just be one more chapter in the rollercoaster ride that is the Trump presidency," they wrote.

But if the North Korean process stalls and Trump's domestic troubles mount, they warned, North Korea may slip down his priority list.