Kulakhmetov did not specifically mention the troops remaining outside Abkhazia, another separatist region.
Russia must pull out its troops from areas surrounding South Ossetia and Abkhazia by Friday under a cease-fire brokered by French President Nicolas Sarkozy. Russia left troops in the areas after they routed Georgian forces during a five-day war in August.
Russian forces have been packing up and dismantling posts outside South Ossetia and Abkhazia in recent days in preparation for the withdrawal.
At a Russian checkpoint near the Georgian village of Kvenatkotsa, about a dozen Russian military vehicles were parked on a hillside Tuesday ready to go. At the Karaleti checkpoint, 20 kilometers south of the South Ossetian border, a crane lifted concrete blocks that had been blocking the road.
A European Union mission monitoring the cease-fire said the pullback would be a "positive" development.
"We will have to verify for ourselves to make sure the deal has been met," said a spokesman for the mission.
Kulakhmetov said Russian troops already had withdrawn most of their equipment from six checkpoints outside South Ossetia, adding that they still have to remove some fortifications and level trenches.
The cease-fire also calls for both sides to return troops to the positions they held before the fighting broke out -- but Russia's plan to keep around 8,000 troops in the regions well exceeds the number deployed there as peacekeepers before the fighting began.
Russia later recognized the independence of South Ossetia and Abkhazia.
President Dmitry Medvedev's foreign policy adviser, Sergei Prikhodko, told reporters that Moscow would insist that representatives of Abkhazia and South Ossetia take part in an international conference set to open in Geneva next week.
Russia sent its forces into South Ossetia in August to repel an offensive by the Georgian government to retake the territory from pro-Moscow separatists who had controlled it for over a decade.
Russian troops then pushed further into Georgia, saying they were needed there to prevent more Georgian attacks.
The West has condemned Russia for a "disproportionate response" to Georgia's actions and has repeatedly demanded that Russia pull its troops out of Georgia's heartland.
Georgian police are due to move in behind retreating Russian forces to avoid a security vacuum that the EU monitors fear could be exploited by militias active in the region.
"There won't be many of us in the beginning because we need to conduct reconnaissance of the territory," Georgian Interior Ministry spokesman Shota Utiashvili said.
AP, Reuters
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