The move comes as leaders of those breakaway regions step up their campaigns for recognition in the wake of the UN-administered province of Kosovo declaring independence from Serbia in mid-February.
Russia's State Duma adopted a resolution on March 21 calling on the Kremlin to recognize Georgia's two Moscow-backed separatist regions if Georgia joins NATO.
"If we see Georgia's accelerated entry into NATO, or a military aggression, then Abkhazia and South Ossetia will unquestionably have the right to unilaterally declare their independence," Aleksei Ostrovsky, the chairman of the Duma's Committee for Commonwealth of Independent States (CIS) Affairs, told reporters ahead of the vote. "I am sure that if the Georgian leadership adopts such measures, the Russian Federation will respond adequately to these measures and will recognize the independence of these republics."
The draft resolution also recommends that Russia open missions in Abkhazia and South Ossetia, ease border restrictions, and boost economic ties with the breakaway regions.
It says that by recognizing Kosovo -- which declared independence from Serbia on February 17 -- the West gave Russia the right to change its policies on Abkhazia and South Ossetia.
The document, drafted by pro-Kremlin lawmakers, is not binding. But its adoption is certain to exacerbate fears that Moscow is preparing to recognize the sovereignty of both provinces, which it has backed diplomatically and economically since they broke away from the Georgian government in wars in the 1990s.
Russia has had peacekeeping troops in Abkhazia and South Ossetia, although Georgia accuses them of favoring the separatist side. Voting in Russia's March 2 presidential election was held in both regions, where most residents have Russian passports.
The two self-declared governments have stepped up their campaign for recognition since Kosovo's declaration of independence. Separatists insist that their regions are ethnically distinct from Georgia.
But Georgian President Mikheil Saakashvili has vowed to bring both provinces back into the fold, a stance supported by the United States and the European Union.
Russia is firmly opposed to Georgia joining NATO. Some political analysts say Moscow is using the threat of recognition to deter the alliance from moving toward granting Georgia membership. Others say Russia will stop short of recognizing Georgia's breakaway regions for fear this could bolster separatist movements on its own territory, particularly in Chechnya.
Saakashvili has applied for a NATO Membership Action Plan, the first step on the road to joining the Western military alliance.
NATO holds its next summit in Bucharest on April 2-4.