The US has condemned Pyongyang's "provocative threats", saying they were "a step in the wrong direction".
Washington has joined China, Russia, Japan and other countries in urging Pyongyang to return to negotiations.
The row follows North Korea's launch of a long-range rocket on 5 April, which critics say was a missile test.
Pyongyang says the rocket put a communications satellite into orbit and has reacted angrily to Monday's statement from the UN Security Council condemning the launch.
It said the criticism was an "unbearable insult" which debased the North Korean people.
On Tuesday, North Korea's Foreign Ministry said it was permanently leaving the long-running six party talks on its nuclear programmes and would "not be bound by any agreement reached at the talks".
The ministry also said it was taking steps to reactivate its partially-dismantled Yongbyon nuclear facility.
The International Atomic Energy Agency (IAEA) said it had been instructed to remove seals and equipment from the Yongbyon reactor and that its monitors had been ordered to leave North Korea .
Interceptions mulled
Pyongyang's move has been criticised by all the other members of the six party talks - the US, China, Russia, South Korea and Japan.
Analysts say South Korea may soon announce that it is signing up to the controversial US-led Proliferation Security Initiative (PSI) in response.
Membership of the PSI would allow South Korea to intercept any ships heading for the North which are believed to be carrying weapons or other items covered by existing sanctions.
On Tuesday, White House spokesman Robert Gibbs called on North Korea "to cease its provocative threats and to respect the will of the international community and to honour its international commitments and obligations".
Mr Gibb's strongly worded response defended the UN statement, and said withdrawing from negotiations was "a serious step in the wrong direction" for North Korea.
US Secretary of State Hillary Clinton has described North Korea's reaction as "an unnecessary response to the legitimate statement put out of concern by the Security Council".
She said she hoped there would be an opportunity to discuss the issue with Washington's partners in the six-party talks, including North Korea itself.
China and Russia - the North's neighbours and closest allies - have already urged North Korea to reconsider its decision, with Beijing calling for "calm and restraint".
Japan, whose territory the rocket flew over, said returning to the talks was the best option for North Korea.
Government spokesman Takeo Kawamura said it would be "smart of North Korea, for the economic revival of the country and in order for Pyongyang to co-exist in the international arena, to humbly listen to international opinion" and rejoin the talks.
Limited options
IAEA inspectors went to North Korea following a landmark deal in February, under which it agreed to end its nuclear ambitions in return for aid and political incentives.
It had carried out a nuclear test in October 2006.
Some progress was made - last year North Korea partially disabled its Yongbyon reactor and handed over what it said was a complete declaration of its nuclear activities.
In return, the US removed North Korea from the list of countries it says sponsors terrorism.
But talks have stalled in recent months, as Washington and Pyongyang accused each other of failing to meet obligations.
Analysts say the action from North Korea appears to be an attempt to test the Obama administration and to force it to make fresh concessions.
The BBC's Kim Ghattas in Washington says that beyond condemning Pyongyang's actions, Washington's options are limited.
North Korea's neighbours, such as Beijing, are more concerned with maintaining its stability while the US wants to ensure Pyongyang remains at the negotiating table.
