North Korea has said it has no interest in meeting the US if their summit is based on "one-sided" demands to give up nuclear weapons.
First vice foreign minister Kim Kye Gwan said that if the US "corners us and unilaterally demands we give up nuclear weapons we will no longer have an interest in talks and will have to reconsider whether we will accept the upcoming DPRK-US summit".
The US-North Korea summit, a historic meeting between US President Donald Trump and North Korea's Kim Jong Un, is scheduled for 12 June in Singapore.
But it now looks to be under threat, with North Korea apparently losing its patience.
On Tuesday night, the North announced it was scrapping high-level talks with South Korea, blaming the South's military drills with the US, which began a few days ago.
Then on Wednesday, in a statement quoted by the state KCNA news agency, Kim Kye Gwan said that the fate of the summit and relations between his country and the US "would be clear" if Washington spoke of a Libya-style denuclearisation for the North.
Mr Trump would also remain a "failed president" if he followed in the steps of his predecessors, the statement added.
Kim Kye Gwan appeared to be responding to recent comments from Mr Trump's security adviser John Bolton and others suggesting that North Korea should follow the "Libyan model" of nuclear disarmament.
Libya cut its nuclear programme in exchange for the easing of sanctions.
North Korea, however, sees the gruesome death of Libya's leader Moammar Gadhafi in 2011 as justification for its own nuclear development amid what it describes as US threats.
If the US-North Korea summit was to be cancelled, it would be frustrating and embarrassing for Mr Trump, who had promised to make it a "very special moment for world peace".
It will also be a blow to optimism inspired by last month's historic meeting between Mr Kim and South Korea's leader President Moon Jae-in.
At that meeting, the first between the two countries in 11 years, Mr Kim pledged a "new history".
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A joint statement said the two had confirmed their goal of achieving "a nuclear-free Korean peninsula through complete denuclearisation".
The statement did not provide any new specific ideas on how to achieve the objective, however.