Georgian authorities said earlier they had launched a police operation in the Kodori Gorge, the only Tbilisi-controlled part of Abkhazia, to disarm a militia led by Emzar Kvitsiani, a former presidential envoy to the area.
Rustavi-2 said police had resumed firing at Emzar Kvitsiani and his supporters after they had been surrounded near a village.
The Georgian Interior Ministry issued an ultimatum to Kvitsiani earlier Wednesday giving him four hours to surrender.
The operation started 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.
Rustavi-2 reported earlier the police had surrounded Kvitsiani and up to 150 members of his militia near a village and nearby forests. About 80 former members of the Hunter battalion laid down their arms after receiving security guarantees from the authorities, the channel said.