In a statement carried by the official KCNA news agency, the North praised Trump for his "willingness" to improve relations with Pyongyang, but said the United States treasury's decision to impose sanctions on three officials over alleged human rights abuses could "block the path to denuclearisation on the Korean peninsula forever".
Denuclearization talks have struggled to progress since Trump and Kim's historic Singapore summit in June.
If Washington believes the policy of increased sanctions and pressure would force the North to give up its nuclear weapons, "it will count as greatest miscalculation, and it will block the path to denuclearization on the Korean peninsula forever", the statement added.
But on Monday (Dec 17) its nuclear assets were conspicuous by their explicit absence from coverage of the seventh anniversary of the death of Kim's father and predecessor Kim Jong Il, on whose watch Pyongyang carried out its first two nuclear tests.
Uncertainty over the talks, however, has risen in recent months amid ongoing sanctions pressure from Washington - pressure that repeatedly has triggered angry rhetoric from Pyongyang.
In a statement carried on the official state media, North Korea's foreign ministry denounced new USA sanctions, including the listing of one of Kim Jong-un's right-hand men.More news: Counting begins to decide fate of in 5 states
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Mr. Jong is minister of state security, Mr. Choe heads the Organization and Guidance Department and Mr. Pak is director of the Propaganda and Agitation Department.
Despite the latest war of words, a second summit between Mr Trump and Mr Kim is expected to be held next year. "The sanctions are on.I'd love to take the sanctions off, but they have to be responsive, too".
The statement, attributed to the policy research director of the North Korean foreign ministry's Institute for American Studies, added that US officials, including those at the state department, were "bent on bringing DPRK-US relations back to the status of a year ago which was marked by exchanges of fire" - a reference to North Korean ballistic missile launches and a nuclear test, as well as angry verbal exchanges between the countries' leaders.
The president also said: "We are doing just fine!"
Despite the request - which have at times been more along the lines of threats - the USA has maintained the crippling sanctions. The meeting has yet to be rescheduled.
A second summit is expected to be held between United States and North Korea next year.