"We are asking the Georgians and the Russians to do everything they can to de-escalate the tensions," Rice told reporters travelling with her from Beijing to Moscow.
Rice, who arrived in Russia on a one-day visit, said she was very concerned about persistent tensions between Tbilisi and Moscow and especially the "frozen conflicts" of breakaway Abkhazia and South Ossetia.
"I think we have been clear with both sides that cooler heads need to prevail here," said Rice, pledging to raise the issue in her meeting with President Vladimir Putin.
The latest crisis between the two former Soviet states stemmed from Georgia's brief detention of four Russian servicemen on suspicion of espionage.
They were released after international mediation but Russia cut sea, air rail and postal links and ordered the deportation of hundreds of Georgians it said were illegal immigrants.
Putin on Friday told European Union leaders in Finland that Georgia was risking bloodshed by seeking to regain control over the regions by military means.
"The rhetoric really needs to be lowered," Rice said. "I would be especially concerned that there would be no rhetoric which might encourage activity -- military, provocative activity in these frozen conflicts of Abkhazia or South Ossetia."
She added: "I think that (military action) is the kind of problem that could get out of control. I will talk to the Russians about that problem."

Copyright Reuters, 2006