Six Russian servicemen, whom Georgia also accuses of espionage and intelligence activities, have already been detained in the South Caucasus country.
Georgian police have surrounded the headquarters of the Russian contingent in Tbilisi, demanding the surrender of Lieutenant Colonel Konstantin Pugachin.
Georgian Defense Minister Irakly Okruashvili said Wednesday the police cordons will be lifted when Pugachin is handed over to the Georgian side.
Russia's Deputy Prime Minister and Defense Minister Sergei Ivanov described the Georgian authorities' actions as "total lawlessness and hysteria."
Tensions between Russia and Georgia have been rising steadily for the past several years over the presence of Russian peacekeepers in the breakaway Georgian republics of Abkhazia and South Ossetia.