"According to our information he is now in Russia," Irakly Okruashvili said. "A few days ago he left Abkhazia."
Georgian troops entered the Kodori Gorge to disarm a rebellious militia unit led by Kvitsiani, a former presidential envoy to Abkhazia. The gorge is the de facto border between Georgia and Abkhazia.
Okruashvili said Kvitsiani was for Georgian law enforcers "a typical criminal on the wanted list, who will sooner or later will have to stand trial."
The Russian Embassy in Tbilisi said earlier that it had no information on Kvitsiani's whereabouts.
Last week the Georgian authorities have announced a reward of $55,000 for the information about the whereabouts of Kvitsiani.
Georgia started what it termed an anticrime operation in the area after Kvitsiani said on July 23 he did not recognize Tbilisi's rule. He said Georgian troops were moving into the area to disarm former members of his Hunter border guard battalion, which was formally disbanded in 2005, although most members refused to lay down their arms.