Georgia's Rustavi television said earlier on Tuesday that Kvitsiani, who had refused to obey orders from Tbilisi Monday, had fled the Kodori Gorge for Abkhazia, and aired an audio recording of an alleged conversation between Kvitsiani and Georgian opposition politician Irakly Batiashvili.
Rustavi said that the taped conversation featured Kvitsiani's voice as saying that the Abkhazian leadership was providing him with weapons and manpower.
Anatoly Zaitsev, chief of Abkhazia's General Staff, said Kvitsiani was not in Abkhazia, and described media reports about his flight to the unrecognized republic as provocation.
"It is merely information warfare," he said, and also denied Georgian television reports about Abkhazia supplying weapons to Kvitsiani.
Zaitsev also said that the Abkhazian Defense Ministry had no information about armed clashes in the Kodori Gorge.
Russia's Rossiya TV channel quoted peacekeepers as saying earlier that an armed clash had broken out in the troubled district.
Russian Defense Ministry spokesman Vyacheslav Sedov later confirmed reports about gunfire being exchanged in the Kodori Gorge.
Georgian Education Minister Alexander Lomaya told the Georgian television that the Interior Ministry was conducting a special police operation in the district.