More than 2,000 soldiers from Georgia and Russia patrol the area under an agreement ending the separatist war between Georgia and the Abkhaz minority in the early 1990s.
Abkhazia is formerly part of Georgia but is now allied with Russia.
The local agencies reported that the defence ministry stressed that the "total number of Russian peacekeepers does not exceed the numerical limits agreed under international agreements".
Russia has said that the extra troops have been placed in Abkhazia because Georgia plans to attack the territory.
It is an accusation Georgia rejects. They have countered that Russia is attempting to annex the region.
Georgia has said the Russian move is provocative and irresponsible.
Separatist forces in the territory are reportedly given financial assistance by Russia.
Thousands of residents of Abkhazia and South Ossetia – which also broke from Tbilisi in the 1990s – have been issued with Russian passports.
Nato warned on Wednesday that the move undermines Georgia's sovereignty.
The White House added to the international concern, saying that the additional troops would increase tension in the province.