Just ahead of her departure for Moscow next week, Rice said the United States and Russia are working well together on a number of issues but that the overall ties remained "complicated" by a rollback in reforms and Russia's contentious relations with its neighbors.
"On many things we have done very well, but the fact is that on some others it's been a difficult period," she said of the U.S.-Russia relationship.
Her comments, in testimony to a Senate Appropriations subcommittee, came a day after Putin delivered oblique but pointed criticism at a Victory Day parade in Red Square of perceived U.S. domination in global affairs, warning the world faces threats like those before World War II.
Rice did not directly address Putin's remarks but said Russia appeared unwilling to accept close U.S. ties with former Soviet states in eastern and central Europe where Moscow has strongly criticized Washington's plans to deploy a missile defense system.
"The Russians, I think, do not accept fully that our relations with countries that are their neighbors, that were once part of the Soviet Union, are quite honestly good relations between independent states and the United States," she said.
Strains over these countries have been exacerbated by what Rice said was a deterioration in democratic progress in Russia after an initial surge following the end of the Cold War.
"It's even more difficult when one looks at what is happening domestically in Russia where I think it's fair to say that there has been a turning back of some of the reforms that led to the decentralization of power out of the Kremlin," she said.
"I think everybody around the world, in Europe, in the United States, is very concerned about the internal course that Russia has taken in recent years," Rice said.
She said "the concentration of power in the Kremlin has been troubling" especially since Russia is due to hold presidential and parliamentary elections next year.
While relations are complicated, Rice said the two former enemies remain on speaking terms, noting that President Bush and Putin continue to have a personal friendship.
"One of the good things about President Bush's very good personal relationship with President Putin is that he can raise those issues and we can talk about them," she said.
Relations between Russia and the U.S. have become increasingly tense amid U.S. criticism of the Kremlin for rolling back on democracy and Moscow's complaints against U.S. plans to deploy missile defense sites in Europe close to its western borders.
In a state of the nation address last month, Putin called for a Russian moratorium on observance of the Conventional Forces in Europe Treaty, which limits the number of aircraft, tanks and other non-nuclear heavy weapons around the continent, saying that NATO members' refusal to ratify an amended version of the pact hurt Russia's security interests.
Putin also threatened to pull out of the treaty altogether unless talks with NATO members yielded satisfactory results, and some Russian generals warned that Moscow could also opt out of a Cold War-era treaty with the United States banning intermediate-range missiles.