Russia says its troops have started pulling back from a "buffer zone" around Georgia's breakaway region of South Ossetia.
A BBC correspondent in the area said he saw Russian forces dismantling and leaving one checkpoint they had set up.
Moscow must pull its troops from areas around South Ossetia and Abkhazia - another breakaway region in Georgia - by Friday under a ceasefire deal.
Russia has kept troops there since ousting Georgian forces in August.
Russian foreign minister Sergei Lavrov told the BBC that Moscow had faith in European Union monitors ensuring security in the buffer zone.
"This is [a] European Union matter and EU cause of pride.... We trust them," he said.
Mr Lavrov said that the Russian military pull-out would be completed on time but that EU monitors would not be allowed to deploy in the two breakaway regions where Russia plans to maintain an 8,000-strong force - South Ossetia and Abkhazia.
A number of Russian armoured personnel carriers were seen heading towards South Ossetia, news agencies report.
The commander of Russian troops on the ground said the withdrawal from all six checkpoints would be completed by the end of the day.
"Everything is completely on track. Everything will be noted and registered in documents," Maj Gen Marat Kulakhmetov said.
The Russian withdrawal is being monitored by some 200 European Union observers.
The pull-back was agreed in a ceasefire deal brokered by French President Nicolas Sarkozy in early August.
But Moscow plans to keep nearly 8,000 troops in Abkhazia and South Ossetia, which it has recognised as independent states.
Western leaders have condemned both the buffer zones and Russia's recognition of the two regions.
The EU wants its observers to have access to the breakaway regions, but Russia has repeatedly refused to guarantee that.
The fighting in the region began on 7 August when Georgia tried to retake South Ossetia by force after a series of lower-level clashes.
Russia launched a counter-attack and the Georgian troops were ejected from both South Ossetia and Abkhazia days later.
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