Vyacheslav Kovalenko said the situation in Georgia's breakaway regions was among topics discussed.
He said Russia was particularly worried about tensions in South Ossetia, where Georgian police and gunmen exchanged fire on January 29, one day after a shelling incident left three South Ossetian police officers injured.
Georgia's government, which has vowed to bring South Ossetia and Abkhazia back under central control, frequently accuses Russia of encouraging separatists.
Kovalenko returned to Tbilisi on January 23, four months after Moscow recalled him over a spying row with Georgia. Russia then also cut air and other transport links and forced hundreds of Georgian migrants to leave Russia.
Kovalenko is to present his credentials to President Mikheil Saakashvili on January 31.
(ITAR-TASS, civil.ge, AP)