The six-point plan to end hostilities requires Russia's troops to pull back to their positions before August 8, but allows its peacekeepers to take "additional security measures" in a buffer zone near breakaway South Ossetia, inside Georgia proper.
"The Russian side has fulfilled the agreements set out in the Medvedev-Sarkozy plan drawn up in Moscow," Defense Minister Anatoly Serdyukov said in a report to President Dmitry Medvedev.
"The units' withdrawal took place without upsets, and was concluded according to plan at 19:50 Moscow time [15:50 GMT]," he said.
The troops have moved back into South Ossetia, and some are already at their bases, he said.
The announcement was immediately rejected by Georgia, as well as the U.S. and French leaders.
White House spokesman Gordon Johndroe told reporters that President George W. Bush and French President Nicolas Sarkozy had discussed the issue over the phone, and agreed that "Russia is not in compliance and that Russia needs to come into compliance now."
Russia has come under severe pressure from Western powers since its peace enforcement operation in response to Georgia's ground and air offensive to regain control over South Ossetia, a small province home to around 70,000 people that broke away from Georgia in the early 1990s.
Large numbers of civilians died in the Georgian onslaught, although figures still remain unclear, and thousands were forced to flee the province, mainly across the border into Russia.
On Tuesday, NATO said it was freezing contacts with Russia until it pulled its troops out of Georgia, and on the same day Western powers submitted a draft United Nations Security Council resolution calling for Russia's immediate withdrawal from Georgia.
Russia responded on Wednesday with its own draft Security Council resolution, reiterating the six-point peace plan signed last week by the parties involved, including the stipulation that Russia may take "additional security measures" in Georgia, while omitting any reference to Georgia's territorial integrity.
The six points agreed by the Russian and French leaders and repeated in the draft resolution include non-use of force, a definitive end to hostilities, free access to humanitarian aid, and a pullback of Georgian troops to their bases.
The remaining points address more controversial issues - the withdrawal of Russian forces to "the line prior to the beginning of hostilities," but only after international mechanisms are set up allowing Russian peacekeepers to "take additional security measures," and also the launch of "an international discussion of lasting security and stability arrangements for South Ossetia and Abkhazia."
Russia's president has said the two breakaway regions should be allowed to make their own decisions on their future status.
