Tank rounds and mortar bombs crashed into opposition districts in the rebellious central city of Homs, killing 17 people, activists said, reporting 14 deaths elsewhere in Syria.
"Thirty tanks entered my neighbourhood at seven this morning and they are using their cannons to fire on houses," said Karam Abu Rabea, a resident in Homs's Karm al-Zeitoun neighbourhood.
One focus of demonstrations was the anniversary of Kurdish unrest in Syria in 2004 when about 30 people were killed.
Many thousands of Kurds demonstrated in northeastern cities, YouTube footage showed, some carrying banners that read "Save the Syrian people". Other clips showed hundreds of protesters in the Assali district of Damascus, burning posters of Assad's father Hafez al-Assad and chanting "God damn your soul, Hafez".
Syria's state news agency SANA reported big pro-Assad demonstrations in Damascus and Hassaka in the northeast.
Tight media restrictions imposed by the authorities make it hard to assess conflicting accounts of events on the ground.
Street protests have swelled every Friday after Muslim prayers since the anti-Assad revolt erupted a year ago, despite violent repression by the military and loyalist militias.
Decisive victory has eluded both sides in an increasingly bloody struggle that appears to be sliding into civil war.
