Moscow's troops continue to operate deep inside the Caucasus republic
Russian President Dmitry Medvedev has said forces will begin withdrawing from Georgia on Monday.
Mr Medvedev made the pledge in a telephone call to French President Nicolas Sarkozy, who brokered a Russian-Georgian ceasefire agreement.
Earlier, the Russian commander of frontline forces in Georgia told the BBC a gradual withdrawal of Russian forces was under way.
Russian troops went into Georgia after fighting erupted over South Ossetia.
Maj Gen Vyacheslav Borisov said he had given the order for Russian soldiers in the village of Igoeti, about 32km (20 miles) from the Georgian capital, Tbilisi, to be replaced by Russian peacekeepers.
But National Security Council Secretary Alexander Lomaia dismissed the move.
"This is just a redeployment," he told reporters in Gori, adding that Russian troops were still "all over the place".
The BBC's Gabriel Gatehouse in Gori, the largest town close to the boundary with South Ossetia, says there is a much-reduced Russian military presence there and that lorries can be seen delivering humanitarian aid.
The scene in one area of central Gori
But he says Russian soldiers still control the town's key entry and exit points.
The Russian commander in Gori says his troops are staying to prevent looting and will leave when Georgian police are ready to take over.
Georgia says its police force would be able to maintain law and order if allowed into Gori, and that the presence of Russian forces so close to the capital is unacceptable.
Russia also controls almost all of the main highway running east-west through Georgia, and major towns along the route.
The conflict between Georgia and Russia erupted on 7 August when Georgia launched an assault to retake South Ossetia, an enclave within Georgia controlled by pro-Russian separatists.
It led to a massive counter-offensive, with Russia moving deeper into Georgia.
The BBC's Sarah Rainsford in Moscow says the Russian pledge looks like a compromise, rather than complete adherence to the terms of the ceasefire, which says Russian troops should return to their pre-conflict positions.
Moscow also says it will only withdraw from Georgian territory once extra security measures are in place.
President Sarkozy, who mediated the ceasefire on behalf of the European Union, has warned Moscow that its forces are barred from any "major urban area" in Georgia.
However, in a letter addressed to his Georgian counterpart, Mikhail Saakashvili, Mr Sarkozy said Russian troops did have the right to patrol "a few kilometres" beyond the conflict zone in South Ossetia.
German Chancellor Angela Merkel held talks with Mr Saakashvili in Tbilisi on Sunday. Afterwards she said she expected a prompt withdrawal of Russian troops.
"We cannot delay this task," she said.
The German chancellor added that Georgia could become a Nato member if it wanted to. Tbilisi's bid to join Nato is fiercely opposed by Russia.
The UN puts the number of those displaced in the conflict at 118,000
The BBC's Richard Galpin, who spent Friday and Saturday travelling from the Black Sea port of Poti to Tbilisi, says Georgian forces seemed to be surrendering control of the highway to the Russians.
In the western town of Senaki, our correspondent saw large numbers of Russian troops moving around on Saturday.
Further east in Zestafoni, he witnessed the panic of residents as the word spread that the Russian army was approaching.
Cars sped away from roadblocks set up by Georgian police, the drivers realising their hopes of reaching Tbilisi had been dashed.
US President George W Bush has said President Medvedev's signing of the truce is "hopeful", but South Ossetia and Abkhazia will remain within Georgian borders, which are internationally recognised.
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