A foreign ministry spokesman also warned that a second Korean war was "unavoidable," with both the US and South Korea refusing Pyongyang's demands to cancel a large-scale joint military exercise next week.
"Now that the US is set to light a fuse for a nuclear war, (our) revolutionary armed forces... will exercise the right to a pre-emptive nuclear attack to destroy the strongholds of the aggressors," the spokesman said in a statement carried by the Korean Central News Agency.
In the past, the North has threatened attacks on US forces in South Korea and also claims to possess long-range missiles capable of carrying a nuclear warhead to the continental US.
The latest threat came two days after the North Korean military announced it would rip up the 1953 armistice agreement ending the Korean War - a move that would theoretically pave the way for a resumption of hostilities.
Tensions have escalated sharply on the Korean peninsula in recent days, ahead of the UN Security Council vote and the annual US-South Korean military exercise scheduled to begin on Monday.
A spokesman for South Korea's defence ministry said that North Korean land, sea and air forces were currently engaged in various training activities and that preparations for another large-scale exercise were apparently being made.
The Security Council is expected to adopt a resolution tightening the UN sanctions screws on North Korea after its widely condemned nuclear bomb test last month.
Amounting to one of the toughest sanctions regimes ever ordered by the UN, the resolution also threatens "further significant measures" if the North stages a new nuclear test or rocket launch.
Pyongyang foreign ministry statement warned that adoption of the resolution would fast track North Korean plans to carry out promised "powerful" countermeasures.
The spokesman also stressed that the decision to "nullify" the 1953 armistice would come into effect when the US-South Korean military drill begins.
"This means that from that moment the revolutionary armed forces will take military action for self-defence against any target any moment," he said.
Meanwhile, North Korean state television has broadcast a massive military and civilian rally in Pyongyang's giant Kim Il-Sung square on Thursday.
The rally was addressed by senior military and party officials who denounced the US and warned that Washington would reap the consequences of its "aggression".