It said other nations should know better why the six-party framework had come to a "definite end", but added that "there is a specific and reserved form of dialogue that can address the current situation", in an apparent call for direct talks with Washington, something Pyongyang has long sought.
Monday's statement follows a comment on Saturday by the North Korean ambassador to the United Nations indicating interest in bilateral negotiations.
"We are not against dialogue. We are not against any negotiation for the issues of common concern," Sin Son-ho said in New York, after declaring: "The six-party talks are gone forever."
North Korea's main Rodong Sinmun newspaper also said on Sunday that the country's envoy told the Asian security conference in Thailand last week that the nuclear standoff was a matter only between Pyongyang and Washington.
The US says it is willing to hold direct talks with the North, but within the six-nation process and only if it returns to the negotiating table and takes irreversible steps towards denuclearisation.
North Korea quit the six-nation talks in April after the UN rebuked the launch of a long-range rocket which the North said was to send a satellite into orbit but which the US and Japan said was a disguised missile test.
Hillary Clinton, the US secretary of state, said last week that the North has "no friends left" to defend it from growing international criticism of its actions.
Clinton held a series of meetings with Asian diplomats at the Asean Regional Forum last week in an effort to enforce the latest UN sanctions ordered in the wake of the North's recent nuclear and missile tests.
Still at war
South Korea has joined the US call for Pyongyang to return to six-party talks.
"The most important thing now is that North Korea should join efforts to resolve the nuclear issue peacefully and should return to the six-party talks as soon as possible," Chun Hae-sung, a spokesman for the unification ministry, was quoted as saying by South Korea's Yonhap news agency.
Monday marks 56 years since the North and South agreed to stop fighting the Korean war.
But the two countries are technically still at war and tensions have been rising in recent months, with Pyongyang abandoning the 1953 armistice and using increasingly bellicose rhetoric against its neighbour.
On Sunday it threatened South Korea and the US with "unimaginably deadly blows" should it come under attack.