The Georgian Interior Ministry says three security officers have been killed and five wounded battling a group of militants who seized hostages in the Lopata Gorge area after entering Georgia from neighboring Russia.
The ministry said 11 militants were killed in the fighting.
The forces secured the release of all 10 Georgian citizens who had been taken hostage and held in three groups.
Officials said at least six militants continued their resistance to the Georgian security forces who had been fighting the militants since late on August 28.
The militants are thought to have entered Georgian from the neighboring restive Russian republic of Daghestan.
The motives of the hostage takers were not immediately clear.
Based on reporting by AFP and Interfax