Rice urged Americans jittery over possible retaliation ranging from bombings to bioterrorism not to panic but made clear that the Sept. 11 attacks on the World Trade Center and the Pentagon had exposed the vulnerable nature of America's open society.
"We're still on a very high state of alert. And I think we're going to remain on a high state of alert for some time," Rice told 60 Minutes' Lesley Stahl.
Rice, speaking four days after the FBI warned there may be new attacks in the next few days either at home or abroad, dismissed media reports that the al Qaeda network of Islamic militant Osama bin Laden may have access to a nuclear device.
"There are reports of all kinds of things, some true and some not. But there's no reason for the American people at this point to fear a specific threat of that kind. We have no credible evidence of a specific threat of that kind," Rice said. "I really want to emphasize it's not specific that there are specific threats underway."
Rice denied suggestions by Stahl that a week of U.S.-led bombing raids on Afghanistan had fueled anti-American sentiments abroad and damaged the international coalition that President Bush has sought to build in his war against terrorism.
"You're seeing thousands of people demonstrate, in countries that have millions of people," Rice said, referring to anti-American protests in Pakistan, Indonesia, Lebanon and other Muslim countries. "I'm not certain the hate for us is growing.''
Rice left open the question of whether military action against Afghanistan might be expanded to Iraq.
"We have a lot of reasons to worry about Iraq and we are monitoring it and watching it very closely. Everybody knows, and the U.S. government has said several times, that Iraq and its people would be better off without (President) Saddam Hussein," Rice said.
© MMI, CBS Worldwide Inc. All Rights Reserved. This material may not be published, broadcast, rewritten, or redistributed. Reuters Limited contributed to this report