They say soldiers have made arrests and fired to keep people indoors.
Opposition websites are showing footage purportedly of a soldier who says he deserted after being ordered to fire on unarmed protesters in Damascus.
Activists say nearly 600 people have died in the crackdown on protests, which began in mid-March.
At least 66 protesters were reported to have been killed, most of them in Deraa, on Friday.
Activists said another six were killed on Saturday when the army seized control of a mosque which had become a centre for anti-government protests in the city.
Deraa has been the focus of government action against the protesters for the last week. Water, electricity and phone lines to the city have been cut.
State television said security forces came under attack on Saturday by "armed terrorists" in Deraa and Homs, Syria's third city.
President Assad's government blames militants and "external forces" for the unrest, which it says have left nearly 80 security personnel dead.
Foreign journalists are not being allowed into the country, and the exact picture of what is happening remains unclear.
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