Rice said the Bush administration in its remaining year would welcome fundamental changes in its dealings with the two countries, as well as with Syria, and as an example pointed to warming ties with Libya, which renounced weapons of mass destruction in 2003.
"The United States doesn't have permanent enemies, we're too great a country for that," she told reporters at a State Department press conference.
But she stressed that neither North Korea nor Iran would benefit from closer relations with the U.S. unless they come clean about their weapons intentions.
The third member of the "axis of evil," Saddam Hussein's Iraq, did not do so to Bush's satisfaction and was invaded in 2003, although no weapons of mass destruction were found. The administration has said it wants to deal diplomatically with the threats it sees from North Korea and Iran.
Rice repeated calls for North Korea to honor its pledge to provide a complete declaration of its atomic programs and to disable all nuclear weapons facilities by year's end, although she left open the possibility Pyongyang would miss the deadline for disabling nuclear sites.
"We have been very clear that we expect a declaration from North Korea that is complete and accurate," Rice said, reiterating Washington's position that the country must describe all of its nuclear activities, including possible sales of equipment to other nations and its alleged dabbling in uranium enrichment to complement a known plutonium program.
Rice would not comment on a report about the discovery by U.S. scientists of uranium traces on aluminum tubes in North Korea, apparently contradicting Pyongyang's claim that its acquisition of the tubes was for conventional purposes. Such tubes could be used in the process of converting hot uranium gas into fuel for nuclear weapons, according to the report in Friday's Washington Post.
Rice said, "We have long been concerned about highly enriched uranium as an alternative (nuclear weapons) route in North Korea."
The declaration is due by Dec. 31, which is also the deadline for disabling North Korea's plutonium plant at Yongbyon. However, diplomats have said the North would likely not be safely able to complete one key disablement step
- removing the fuel rods from its reactor - for several months.
"I sincerely hope it will be by the end of the year, but the key is to get this process right," Rice said.