NATO has urged Russia to reverse its decision and respect Georgia's territorial integrity.
NATO ambassadors said the alliance "condemns the decision of the Russian Federation to extend recognition to the South Ossetia and Abkhazia regions of Georgia and calls upon Russia to reverse its decision."
Dmitry Rogozin instead urged NATO members to reconsider their recognition of Kosovo.
"I am calling on NATO countries to withdraw and review their decision concerning Kosovo's independence - otherwise NATO's peacekeeping mission in the Balkans will be called into question," he said.
Commenting on the NATO ambassadors' statement, he said the alliance "should act on the premise that this is the new political reality."
President Dmitry Medvedev signed decrees on Tuesday recognizing South Ossetia and Abkhazia as independent states, saying recognition was necessary to protect the republics from Georgian acts of aggression, following the August 8 military offensive in South Ossetia.
Western leaders have condemned Russia's decision, which has sparked fears of a new Cold War. U.S. President George W. Bush said in a statement on Tuesday: "Russia's action only exacerbates tensions and complicates diplomatic negotiations."