The Trump administration is hopeful its summit with North Korea will go ahead, despite threats of cancellation.
A White House spokesperson said the US president remained ready.
Hours earlier, North Korea released an angry statement saying it might pull out of the meeting if the US insisted it gave up its nuclear weapons.
The highly anticipated meeting between Mr Trump and North Korea’s Kim Jong-un is due to take place on 12 June.
“The president is ready if the meeting takes place,” said White House spokesperson Sarah Sanders. “If it doesn’t, we’ll continue the maximum pressure campaign that’s been ongoing.”
When asked if it would go ahead, Mr Trump later said: “We’ll have to see”.
He reiterated that the US would still insist on denuclearisation.
The groundbreaking agreement for Mr Kim and Mr Trump to meet came about as North Korea said it was committed to denuclearising the Korean peninsula.
Exactly what that would entail has remained unclear but North Korea has invited foreign media to witness the dismantling of its main nuclear test site later this month.
What suddenly upset North Korea?
North Korea’s statement, carried by state media, said the country had had high expectations from the summit, but it was “totally disappointed” by recent reckless remarks from the US.
It pointed the finger squarely at US National Security Adviser John Bolton.
“We do not hide our feeling of repugnance towards him,” said the statement, which was written by Vice-Foreign Minister Kim Kye-gwan.
In a television interview at the weekend, Mr Bolton said North Korea could follow a “Libya model” of verifiable denuclearisation, but this alarms Pyongyang, which watched Libya’s Colonel Gaddafi give up his nuclear programme only for him to be killed by Western-backed rebels a few years later.
A sudden change in tune
By Laura Bicker, BBC News, Seoul
The whole reason the North Korean state has spent years building up a nuclear arsenal, at such a great cost, is for survival.
So to compare denuclearisation in North Korea with Libya or indeed Iraq as John Bolton did on Sunday is not going to offer much comfort. Both regimes collapsed.
This is also a warning shot to the Trump administration. They will be aware how much Mr Trump wants this summit and how it is being spun as a success brought about by his maximum pressure strategy.
There were signs this boasting irritated Pyongyang, but now it has decided to speak out through someone in a position of power.
North Korea wants the world to know that it is coming to the negotiating table from a position of strength, and they may feel that they are making all the concessions.
They’ve suspended all missile tests, released the three US detainees, Kim Jong-un met President Moon and the pair signed a declaration, and they’re about to dismantle a nuclear test site in front of international media.
So to hear the Trump administration claiming credit for a deal they don’t like has been a step too far.
These statements more than hint that North Korea is prepared to walk away from President Trump’s summit in Singapore until it does hear a deal it does like.
What does North Korea’s statement say?
Kim Kye-gwan said: “If the US is trying to drive us into a corner to force our unilateral nuclear abandonment, we will no longer be interested in such dialogue.”
The vice-foreign minister is known to be highly respected in the North Korean leadership and has taken part in negotiations with the US before. There is very little chance his comments were not personally endorsed by Kim Jong-un.
Hours before the announcement, in a sign of growing problems, North Korea had also pulled out of a meeting scheduled with South Korea on Wednesday because of anger over the start of US-South Korea joint military drills.
A Chinese government spokesman urged North Korea and the US to “meet each other halfway” ahead of negotiations.
Why the personal attack on John Bolton?
The hawkish conservative is a firm defender of US power and a confrontational advocate for wielding that strength abroad. He has previously said it would be “perfectly legitimate” to carry out a pre-emptive strike on North Korea.
In media interviews over the weekend, he said North Korea could follow a Libyan model of nuclear disarmament – Libya gave up its weapons’ programmes in the early 2000s and only then secured economic aid and normalised relations with the US.
However during the 2011 uprising against Colonel Gaddafi’s regime, Western powers intervened in Libya in favour of the rebels, and Gaddafi was captured and killed.