North Korea has said it is still willing to talk "at any time in any form" after US President Donald Trump abruptly cancelled his meeting with Kim Jong-un.
Vice-foreign minister Kim Kye-gwan said Mr Trump's decision was "extremely regrettable".
President Trump blamed the North's "open hostility" for the cancellation.
The summit would have been the first time a sitting US president had met a North Korean leader.
The details of the meeting in Singapore on 12 June were unclear. But talks would have focused on ways of denuclearising the Korean peninsula and reducing tensions.
Just hours before Mr Trump's announcement, North Korea said it carried out its promise to dismantle tunnels at its only nuclear test site.
Mr Trump announced the cancellation in the form of a letter personally addressed to Mr Kim.
A senior administration official in the US later gave further details, saying North Korea had shown "a profound lack of good faith".
There were a series of "broken promises" from Pyongyang, the official told reporters, including when the White House sent the deputy chief of staff to Singapore to meet North Korean diplomats ahead of the summit.
"The North Koreans didn't show up. They simply stood us up."
The official also said President Trump had "dictated every word" of his letter to Kim Jong-un after talking with South Korean President Moon Jae-in.
What did Mr Trump's letter say?
Mr Trump said he had been "very much looking forward" to meeting Mr Kim.
"Sadly, based on the tremendous anger and open hostility displayed in your most recent statement, I feel it is inappropriate, at this time, to have the long-planned meeting," Mr Trump said in a letter to Mr Kim.
"You talk about your nuclear capabilities, but ours are so massive and powerful that I pray to God they will never have to be used," he added.
But he called the meeting a "missed opportunity", saying "someday, I look very much forward to meeting you".
In a later statement at the White House, Mr Trump said the step was a "tremendous setback for North Korea and the world", adding the US military was "ready if necessary" to respond to any "reckless" act from North Korea.
What was he referring to?
Mr Trump was apparently responding to statements from a senior North Korean diplomat attacking his administration and casting doubt over the meeting.
Choe Son-hui had said the suggestions from US Vice-President Mike Pence that North Korea "may end like Libya" was "stupid".
Ms Choe, who has been involved in several diplomatic interactions with the US over the past decade, said the North would not "beg" for dialogue and warned of a "nuclear showdown" if diplomacy failed.
A White House official quoted by Reuters described the comments about Mr Pence as the "last straw". They stressed, however, there was a "backdoor that's open still".
References to Libya have angered North Korea. There, former leader Colonel Gaddafi gave up his nascent nuclear programme only for him to be killed by Western-backed rebels a few years later.
North Korea says that, unlike Libya, it is a fully fledged nuclear state. It is insistent it will not engage in any peace process that jeopardises its leadership or its survival as a state.
What's the reaction been?
South Korean President Moon Jae-in said he was "very perplexed" and that it was "very regrettable" that the summit was not going ahead.
It was South Korean officials who first informed the US earlier this year that Mr Kim was prepared to discuss potential nuclear disarmament.
In April, the leaders of both Koreas had a historic meeting at the border, promising to end hostilities and work towards the denuclearisation of the Korean peninsula.
UN Secretary General Antonio Guterres said the US and North Korea should not give up, saying "nerves of steel" were required.
In the US, Republican Senator Tom Cotton praised President Trump for "seeing through Kim Jong-un's fraud". But Democratic Senator Brian Schatz said the move was what happened "when amateurs are combined with warmongers".