President George Bush had suggested earlier this week a written guarantee that Pyongyang would not be attacked if it gave up its atomic weapons programme.
"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 Democratic People's Republic of Korea and aimed to play a positive role in realising the proposal for a package solution on the principle of simultaneous actions," a North Korean foreign ministry spokesman said.
"Simple and clear is our request," the spokesman said.
The latest comments circulated by the official news agency KCNA signify a clear softening of North Korea's stand.
"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 Democratic People's Republic of Korea"
North Korean spokesman
Earlier, the North had insisted on a non-aggression treaty as an essential pre-condition.
"What we want is for both sides to drop guns and establish normal state relationship to co-exist peacefully. 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," the spokesman said.
He further said that North Korea had been in touch with the US through its diplomats at the United Nations.
The offer made by Bush during this week's Asia-Pacific Economic Cooperation (APEC) summit in Bangkok for a security guarantee to the North, opened up opportunities for resolving the nuclear stand-off in the Korean peninsula.
Accused of developing nuclear weapons, the communist North has always maintained it has the right to arm itself against external aggression.