The unrest began Friday after the cleric, Sheikh Wahid al-Balous, was killed along with at least 27 others in the twin bombings, activists said. There was no immediate claim of responsibility for the bombings, but some residents blamed the government.

The unusual events underscored the strains growing even in areas that have traditionally supported President Bashar al-Assad or tried to remain neutral during the primarily Sunni insurgency against him.

Those tensions have ballooned even as Mr. Assad portrays himself as a protector of minorities like the Druse, and the events in Sweida came after a week of sit-ins and demonstrations to protest the worsening conditions in a number of government-held areas.

One explosion struck Sheikh Balous’s convoy and another hit the hospital where victims were taken, killing some relatives who had gone to check on them, according to residents and activists. According to the Syrian Observatory for Human Rights, a group based in Britain that monitors the conflict with the help of a network of contacts in Syria, 28 people died in the bombings and nine were killed in the clashes, including the six security personnel.

“We are between two fires, the regime and Daesh,” said Abu Tayem, an antigovernment Druse activist in Sweida, using the Arabic acronym for the Islamic State group, also known as ISIS or ISIL, whose militants have slaughtered minorities in areas they take over.