The announcement came after Alexander Lomaia, Georgia's security council chief, said Russia had pulled out of a position in the town of Ganmukhuri, outside of Abkhazia - one of 24 positions in Georgia that officials say are still held by Russian forces.
Lomaia said three or four armoured personnel carriers and a few dozen troops remained in Ganmukhuri.
Russia established diplomatic relations with Abkhazia and South Ossetia on Tuesday and Lavrov said he and his counterparts have agreed treaties to strengthen ties.
Sarkozy, left, and Medvedev, say they have revised their agreement [AFP]
On Monday, Dmitry Medvedev, Russia's president and Nicolas Sarkozy, the French president, revised the European Union-brokered deal to end the fighting between Russia and Georgia.
The deal with Sarkozy is expected to lead to the deployment of at least 200 EU monitors in the area surrounding the two breakaway regions by next month.
The agreement obliges Russia to pull out of those regions in 10 days following the deployment of monitors.
Lavrov said the deal - accompanied by EU guarantees that Georgia would not use force against the two provinces - was a victory for Russia.
He said Abkhazia and South Ossetia will be represented at an international conference on security in the region in Geneva next month.
War erupted between Georgia and Russia erupted on August 7 when Georgia launched an attack to regain control over South Ossetia.
Russia sent in troops who quickly routed the Georgian forces and pushed deep into Georgia.