The Federal Security Service said one of its officers and two Georgians who it believes were security agents were killed in clashes near the de-facto administrative border between Georgia and its breakaway region of Abkhazia.
The FSB said Friday that a Russian border troops unit was attacked with automatic weapons while on a reconnaissance mission.
"In the course of the conflict, the attackers were destroyed," the FSB said in a statement.
"According to the Abkhaz security service, the two people killed were members of the intelligence unit of the Georgian Interior Ministry's anti-terrorist center," it said.
Georgia's Foreign Ministry said in a statement that the two Georgians killed were criminals and were wanted in Georgia for robberies and kidnappings.
It said the incident was a "criminal feud."
"This criminal incident confirms once again that the parts of Georgia occupied by Russia have been turned into criminal black holes," the Georgian ministry said.
Russia and Georgia fought a brief war in 2008 after the Georgian army's incursion into another breakaway region, South Ossetia. Moscow recognized both regions as independent after the war.
Russia has troops in both regions and provides them with generous financial aid.