An EU official has voiced fears that Russia may recognise Georgia's breakaway republic of Abkhazia.
Russia announced last week it was lifting trade restrictions on Abkhazia which then called for recognition of its self-declared independence.
EU External Relations Commissioner Benita Ferrero-Waldner said there was a "growing pre-occupation and anxiety" that Moscow was planning recognition.
Georgia has accused Russia of encouraging separatism.
Ms Ferrero-Waldner said: "Georgia's territorial integrity has always been clearly supported by the EU... this is absolutely clear."
She said Sweden and Poland had written to the EU to ask for more to be done to maintain stability in Georgia before parliamentary elections there in May.
Russia has said its position on Georgia's territorial integrity is unchanged.
Leonid Slutsky of the Russian Duma's international affairs committee told the Itar-Tass news agency that Moscow did "not want to split the country, but we are asking it to face the truth".
A second breakaway republic in Georgia, South Ossetia, also called for recognition of its declaration of independence last week.
Analysts have linked the declarations to Kosovo's proclamation of independence in February which was strongly criticised by Russia.
Both republics fought wars with the rest of Georgia in the early 1990s. Tens of thousands of ethnic Georgians were driven from their homes in Abkhazia.
Georgia fears that Russia's decision to lift sanctions imposed in 1996 will enable Moscow to send weapons or even mercenaries to Abkhazia.