"The bombing and fighting between the regime forces and IS have intensified during the evening and are continuing," said Rami Abdel Rahmane, head of the Syrian Observatory for Human Rights.
"The regime is advancing to the north and northeast of Sweida", adjacent to the desert zone of the southern province, he told AFP.
This military operation would be "the start of a regime offensive to dislodge IS from this pocket" in the Badiya desert of Sweida, he said, adding that "a major military reinforcement (of regime troops) is massing" in the area.
The fighting comes as Russia failed in its negotiations to free some 30 civilian hostages of the Druze religious minority taken by IS last month. The kidnappings followed a series of coordinated attacks against Sweida province which left more than 250 people dead.
On Sunday, the Observatory and news website Sweida24 announced that IS had decapitated one of the hostages, a 19-year-old male student.
This execution, the first since the abductions, came "after the failure of the negotiations with the regime forces", according to the Observatory.
The Syrian Democratic Forces, an Arab-Kurd alliance which fought against IS with the support of the United States, indicated Sunday that it was ready to exchange with IS captured jihadists for the remaining Druze civilian hostages.
Meanwhile IS, which has not claimed responsibility for the execution or the kidnappings, has been pounded by multiple offensives in Syria and today controls less than three percent of the territory.
However, it continues to launch attacks like the bloody strike and kidnappings in Sweida.
The Syrian conflict which began in 2011 has claimed more than 350,000 lives and left millions displaced or fleeing as refugees.