Three Georgian soldiers and 11 suspected militants have been killed in an army operation along the border with Russia, Georgian officials said.
Georgia deployed forces to free several people taken hostage by the gunmen.
The gunmen had crossed from the Russian republic of Dagestan, where armed Islamist insurgents operate, Georgia's interior ministry said.
Correspondents say there are fears the incident could increase tensions between Russia and Georgia.
According to Georgia's deputy interior minister, Nodar Kharshiladze, the militants released the hostages, but opened fire when they were asked to surrender.
"At this point we do not know who these people are and why they entered Georgian territory," Mr Kharshiladze was quoted as saying by AFP news agency.
The BBC's Damien McGuinness in Tbilisi says it was crucial for Georgia to act decisively, as there were fears in Tbilisi that Moscow would use any sign that terrorists from the North Caucasus are operating in the region as a pretext for moving in to Georgia.
In 2008 Georgia and Russia went to war over the Georgian breakaway region of South Ossetia, and the two countries still have no diplomatic relations.
The volatile region of Dagestan has seen some of the worst militant violence in the North Caucasus in recent years.
On Tuesday, a Muslim cleric and six others were killed by a female suicide bomber posing as a pilgrim.