Al Jazeera's Andrew Potter said that Russia claimed that Georgia was informed of the troop movement and called the incident "a provocation".
Relations between the two nations have been dangerously strained in recent months by Georgia's drive for NATO membership and Russia's support for separatists in Abkhazia and South Ossetia - another Georgian region that has de-facto independence.
The tensions have raised fears of military conflict in Georgia, whose location on a key oil export route makes it a focus of contention between Moscow and the West.
Russians detained
Georgia also detained five Russian peacekeepers along the administrative border with the Abkhazia region overnight after an accident involving an armoured personnel carrier.
Shota Utiashvili, Georgian interior ministry official, said that the five peacekeeping officials were detained on Sunday when their armoured personnel carrier collided with a Georgian woman's car, in the town of Zugdidi.
Utiashvili said that the peacekeepers were later released.
Alexander Diordiev, a Russian peacekeeping official, confirmed the detention of the Russian soldiers but denied that there had been any sort of a collision.
"This is the latest attempt by the Georgians to discredit Russian peacekeepers. The police provoked our peacekeepers with their actions," Diordiev said.
Russia accused Georgia on Friday of supporting armed rebels in southern Russia.
Georgia said it would block negotiations on a Russian entry to the World Trade Organisation unless Moscow reversed last month's decision to strengthen ties with the Georgian regions of Abkhazia and South Ossetia.