Givi Targamadze, the head of parliament's Defense and Security Committee, said that the raid in the gorge was being interrupted because of heavy fog and darkness.
Georgian forces are attempting to disarm the militia of Emzar Kvitsiani, a former regional governor. Kvitsiani is the leader of the Hunter militia, which is estimated to number up to 400 men.
Kvitsiani says he is defending the rights of the local Svan people.
Up to 1,000 Georgian troops have been reported deployed in the area.