Law enforcers are seeking to detain militia head Emzar Kvitsiani, a former presidential envoy, and about 50 of his supporters who were surrounded Wednesday near a village in the Kodori Gorge, the only Tbilisi-controlled part of Abkhazia.
The breakaway region declared independence in 1992, which led to a conflict with Georgia that ended with a ceasefire two years later. Thousands died during the fighting.
Georgia started the current operation after Kvitsiani said he did not recognize Tbilisi's rule on Sunday. He said Georgian troops were moving to the area to disarm former members of his Hunter border guard battalion, which was formally disbanded in 2005, though most members refused to lay down their arms.
Georgia's authorities have repeatedly said the operation is not a military one, is only aimed against criminal groups in the region and will not spill over into Abkhazia.