Fried said he hoped the two neighbors would make efforts to improve their relations.
Russia has deported hundreds of Georgian migrants, claiming they were staying in the country illegally, in retaliation for Georgia's brief detention of four alleged Russian spies last month.
Moscow also has imposed a transport and postal blockade on its southern neighbor.
Fried also said Washington will not recognize the independence of Georgia's breakaway republics of Abkhazia and South Ossetia.
The comment came after Abkhazia's parliament sent an appeal to the Russian president and parliament asking for recognition as an independent state.
Russian military hardware being withdrawn from a Russian base in Batumi, Georgia, in August 2005 (TASS)
WHAT COMES NEXT? Although Russia is unlikely to push an aggressive military response to the current tensions with Georgia, it has a number of economic, political, and diplomatic options at its disposal. Already on October 1, Russian President Vladimir Putin summoned his inner circle to weigh Moscow's options... (more)