The fighting was focused around the town of Hamidiyeh in Quneitra province near the disputed frontier with Israel, according to the Britain-based Syrian Observatory for Human Rights.
The Observatory said there were casualties on both sides but did not have exact figures.
Syria's state news agency said the military killed "many terrorists" and destroyed a heavy machine gun in the fighting. The government refers to those trying to oust President Bashar Assad as terrorists.
Heavy clashes have raged in the area since Syrian rebels captured a border crossing near the abandoned town of Quneitra on Wednesday. One day later, fighters from al-Qaeda's Syria branch, the Nusra Front, abducted 45 Fijian peacekeepers and surrounded two Filipino contingents serving in the UN mission that monitors the buffer zone between Israel and Syria.
More From This Section
Fiji's military commander said today that the Nusra Front has issued three demands for the release of the Fijian peacekeepers.
Brig Gen Mosese Tikoitoga said the Nusra Front wants to be taken off the UN terrorist list, wants humanitarian aid delivered to parts of the Syrian capital Damascus, and wants compensation for three of its fighters it says were killed in a shootout with UN officers Tikoitoga said the UN has sent hostage negotiators to Syria.
Ireland, which contributes a 130-member armored rapid response unit to the UN mission, warned yesterday it would not replace its troops next month if UN leaders in New York do not agree on strengthening the force's firepower, command and control, and rules of engagement.
"I've made it very clear that I'm not going to continue to commit Irish troops to this mission unless there's a very fundamental review of how it's going to operate. Clearly this is no longer a demilitarized zone," Irish Defense Minister Simon Coveney told RTE state radio in Dublin.