North Korea unsealed its Yongbyon nuclear reactor last year
North Korea says it is prepared to consider a US offer of a security guarantee to end the deadlock over its alleged nuclear weapons programmes.
President George Bush last week proposed a written guarantee that the US and North Korea's neighbours would not attack if it dropped the programme.
On Tuesday, North Korea said it would settle for nothing less than a formal non-aggression treaty.
North Korea fears it may be attacked - despite US assurances to the contrary.
Mr Bush aired his proposal of a written security guarantee from the US, China, Russia, Japan, and South Korea during a meeting of the Asia-Pacific Economic Co-operation (Apec) meeting in Bangkok earlier this week.
Despite the initial rejection, the latest statement from Pyongyang is more positive.
The North Korean foreign ministry spokesman told the official KCNA news agency: "We are ready to consider Bush's remarks on the 'written assurances of non-aggression' if they are based on the intention to co-exist with the DPRK (North Korea) and aimed to play a positive role in realising the proposal for a package solution on the principle of simultaneous actions."
The ministry spokesman said it had a "simple and clear" request.
"What we want is for both sides to drop guns and establish normal state relationship to co-exist peacefully," he said.
"The unilateral demand that one of the two belligerent parties forces the other party to drop guns and come out first with its hands up can never be met."
Mr Bush has ruled out North Korea's demands for a non-aggression treaty, which would require Congressional approval and could tie Washington's hands in a conflict.
Exactly what kind of security guarantee the US is willing to offer will still have to be negotiated, says the BBC's Jonathan Head.
But Pyongyang's positive language raises the possibility that inconclusive multilateral talks over its nuclear ambitions may be resumed, says our correspondent.
The latest development comes as a delegation from China's Communist Party is visiting North Korea in an effort to restart the talks.
The official Chinese news agency Xinhua described the trip as a good will visit but gave no more details. One of China's most senior leaders, Wu Bangguo, is also due in Pyongyang next week.
In August, six-nation talks in Beijing ended without a settlement or a date to meet again.
Since then North Korea has said it has reprocessed 8,000 nuclear fuel rods and was strengthening its nuclear deterrent.
North Korea responded to Mr Bush's calls for fresh talks during the Apec meeting by test-firing a short range missile.
The crisis began last October when US officials said North Korea had admitted to having a secret nuclear programme, in defiance of a 1994 agreement.