"It is not an easy time in the relationship, but it is also not, I think, a time in which cataclysmic things are affecting the relationship or catastrophic things are happening in the relationship," said Rice, who flew into Moscow on Monday. 
Her talks with Putin are expected to focus on US plans to build a missile defence shield in Europe, as well as a US-backed plan to grant effective independence to the Serbian province of Kosovo after nearly eight years of UN administration.
Russia objects to both proposals, saying it does not see a threat that requires a missile shield in Europe and arguing that to force Serbia, traditionally a Russian ally, to give up Kosovo sets a bad precedent.
However, Rice said Washington and Moscow were working together well in trying to restrict the nuclear programmes of Iran and North Korea.
Growing list of disputes
Steinmeier, who is in Moscow for separate talks with the Russian president on Tuesday, is also expected to discuss Kosovo, as well as a growing list of disputes involving Russia and new EU members, which were once in the Soviet orbit.
An EU-Russia summit set for Friday is likely to be undercut by disagreements over everything from Russia's ban on Polish meat imports to its anger at Estonia's recent removal of a Soviet monument from Tallinn city centre.
Steinmeier said on Monday that it was unlikely Russia and the EU would agree at the summit to start negotiations on an ambitious partnership pact due to cover trade, energy, human rights and foreign policy.
Russia is increasingly suspicious of US and EU activity in its former sphere of influence.
Last week, Putin compared the Bush administration "disrespect for human life and claims to global exclusiveness" to "the time of the Third Reich".
Later, the Kremlin said Putin had not meant to compare the Bush administration's policies with those of Nazi Germany, but the reference highlights Russia's annoyance at what it sees as US domination of world affairs and outsiders meddling in Russian politics.