Regime forces bombed districts in Deraa city and two other towns with despite a ceasefire on Monday.
Syrian regime media said the assault was against Daesh.
The Syrian Observatory for Human Rights, a Britain-based war monitor, said the assault in as-Suwayda province began on Monday morning, almost 24 hours into an internationally brokered ceasefire.
Activists also reported clashes in al Manshyia district in Deraa city.
"The regime attacked an area northeast of as-Suwayda city, backed by air strikes," the monitor said, reporting clashes between government troops and rebels on the ground.
Observatory director Rami Abdel Rahman said the groups under attack have been receiving support from the US-led coalition fighting Daesh.
He said the regime had captured a string of hilltops and villages in the area.
But Syrian regime media named those same positions as territory that government forces had captured from Daesh.
"Our forces and allies captured several areas, villages, hilltops and commanding positions in the eastern countryside of as-Suwayda after eliminating large numbers of Daesh terrorists," regime news agency SANA said.
The clashes come as a ceasefire for southern Syria negotiated by the United States, Russia and Jordan entered its second day.
So far, the deal announced on Friday covers three provinces: Daraa, Quneitra and as-Suwayda.
But in addition to clashes in as-Suwayda, there have been other limited violations according to the observatory, including regime shelling and exchanges of fire with rebels in Daraa.
In Quneitra province, there were also reports of sporadic machine-gun fire from both sides, though there were no casualties in any of the incidents, the monitor said.
Sunday's ceasefire went into effect just ahead of new peace talks in Geneva.
More than 320,000 people have been killed in Syria since the conflict began in March 2011 with anti-government protests.