Paata Dedianashvili said there were no casualties on the Georgian side.
Marat Kulakhmetov, the commander of the Joint Peacekeeping Force, confirmed the shootout.
Four people were killed Friday in a shootout near the Ossetian village of Tbet.
A Russian Foreign Ministry official said the shootout would be discussed at the next meeting of the Joint Control Commission.
"I believe that the latest incidents in South Ossetia - the downing of a Georgian helicopter Sunday and today's shootout in the conflict zone - mean that an early meeting of the Joint Control Commission has to be called," said Yury Popov, a special envoy to the area.
He said the next JCC meeting would be held on September 14-15 in Tskhinvali, the capital of South Ossetia, adding that the incidents would also be discussed at his bilateral consultations with Merab Antadze, Georgia's state minister for conflict resolution.