Eleven militants and three special forces personnel were killed on Wednesday near the Georgian-Russian border, the Georgian Interior Ministry said.
Another six militants have been encircled and action is being taken to detain them, the ministry added.
Interior Ministry units earlier sealed off a gorge near the border with Russia’s North Caucasus republic of Dagestan where an armed group was detected on Tuesday.
According to Georgian media reports, some 20 well-armed militants trespassed into the country’s territory from Dagestan, taking about 10 locals hostage, who were later released.
A special police operation in the village of Lapanquri, eastern Georgia, is ongoing.