Russia said the move would not help ease the crisis between the two caused by their five-day war this month.
"We regret this step from the Georgian side. It will not assist our bilateral relations," Andrei Nesterenko, the Russian foreign ministry spokesman, said, according to Interfax news agency.
Eka Tkeshelashvili, the Georgian foreign minister, said it "would be very awkward to have a diplomatic relationship ... with Russia, when Russia will be setting up diplomatic relations with South Ossetia and Abkhazia."
Speaking to reporters in Stockholm, she said a diplomatic rupture would be a temporary measure that could be ended after Russia stopped occupying Georgian territory.
Russia has turned its campaign against the West, strongly ttacking criticism from Nato and the Group of Seven industrialised powers.
|Tbilisi sets Russia occupation of Georgian territories as the cause of the split with Moscow
The G7 - Britain, Canada, France, Germany, Italy, Japan and the United States - had called on Russia to "implement in full" a French-brokered peace plan and pull all forces out of Georgia.
A Russian foreign ministry statement accused the G7 of being "biased" in favour of Tbilisi and seeking to "justify Georgian acts of aggression".
Nato has also strongly condemned Russia's actions in Georgia, but Nesterenko hit back saying the Western alliance had "no moral right to the role of mentor in matters of international relations and to judge the actions of other states".
Nato is putting "unacceptable pressure" on Russia, Nesterenko said, in an apparent reference to the presence of alliance ships in the Black Sea, including several US naval vessels delivering aid to Georgia.
An emergency EU summit is to be held on Monday and the French presidency said sanctions would not be called for, contradicting comments made on Thursday by Bernard Kouchner, the French foreign minister.
Russia appealed for "reason" to prevail at the summit and for EU leaders to avoid the "path of confrontation."Assurance
"We hope that reason will prevail over emotions," Nesterenko said.
But Igor Sechin, Russia's deputy prime minister, insisted that Russia's massive oil and gas supplies to Europe would not be affected by the Georgia tensions.
Britain and Germany have led calls for measures to reduce Europe's heavy dependency on Russian oil and gas.
"Even during the Cold War, regardless of political or other circumstances, the Soviet Union always promptly met its contractual obligations to deliver energy to Europe, and Russia, being a responsible and reliable partner, will also uphold such principles," Sechin was quoted as saying by Interfax news agency.
Russia maintains it has completed a troop withdrawal from inside Georgia, in line with a ceasefire accord brokered by French President Nicolas Sarkozy, and that remaining troops are on a "peacekeeping" mission.
But it has faced relentless international pressure, which has brought relations with the United States and its allies to a post-Cold War low.
The war of words between Russia and the West hit a new peak when Vladimir Putin, the Russian prime minister, accused the United States of provoking the conflict, in an interview to CNN.
Putin said the US administration had a hand in the war that erupted after Georgian forces tried to take back control of South Ossetia, and drew a link with the US presidential campaign.