"It [Russia] needs to be a part of resolving the problem and solving the problem and not contributing to it," Rice said. "I have said it to the Russians publicly. I have said it privately," Rice told a news conference in Tbilisi.
Rice's visit to Georgia is taking place amid rising tensions between the ex-Soviet Caucasus country and its breakaway regions, Abkhazia and South Ossetia, which have recently seen several explosions, border clashes and disputes over peacekeepers.
The provinces have been a point of contention between Georgia and Russia. Moscow has provided aid to the regions and recently sent additional peacekeepers into Abkhazia saying they are needed to deter new bloodshed, and accusing Tbilisi of escalating the conflict. Georgia has charged Moscow with trying to annex its territory.
Rice urged a peaceful solution to the disputes. "It is very important that all parties reject violence as an option. There must be a peaceful solution," she said.
Four people were killed in a cafe explosion in Abkhazia on Sunday and two died in a clash between Georgian troops and South Ossetian forces last week.
Rice said she would be seeking high-level talks to try and reach a solution to the long-running conflicts in Georgia.
The U.S. top diplomat also expressed support for Georgia's NATO bid, saying the country would hopefully be admitted in a Membership Action Plan in December, paving the way to full membership of the alliance.