Tensions have risen over troop deployments and U.S. plans for missile defense in Europe, and the White House said Bush called Putin ahead of Rice's trip which is intended to calm the situation.

White House press secretary Tony Snow said they talked about Rice's trip, an upcoming June summit in Germany of leaders from the Group of Eight industrialized nations and ``a range of important bilateral and international issues.''

He did not elaborate but the conversation came as Rice said Putin's moves to consolidate power and Russia's testy ties with its neighbors were troubling to the United States and its European allies.

Before her Sunday departure, Rice told lawmakers the U.S. and Russia are working well together on a number of issues but the overall relationship was ``complicated'' by a rollback in reforms and Russia's treatment of nearby states.

``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 that the world faces threats like those from the Nazis before World War II.

Both the White House and State Department later said that Russian officials had told U.S. diplomats in Moscow that Putin's reference to the ``Third Reich'' in his speech was not aimed at the United States.

``They've pointed out that he did not explicitly mention the United States, and they confirmed in a phone call that there's no intent to compare U.S. policies with those of the Third Reich,'' Snow said.

State Department spokesman Sean McCormack said the U.S. accepted the explanation.

Rice did not 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 improvement 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.