Fighting has gone on around the strategically important town, near the Lebanese border, for weeks. Control would give the government access from the capital to the coast, the BBC reports.
Syrian state TV says government troops have surrounded the town and captured key buildings, a claim denied by rebels.
Opposition activists say government air strikes and heavy shelling have killed 50 people, while state media says 70 "terrorists" are dead.
Lebanese militants are said to be involved - Hezbollah siding with the government, Sunni gunmen with rebels.
The assault began early on Sunday with artillery fire and air strikes. In recent weeks the Syrian military has won back surrounding villages and countryside and had encircled Qusair.
