Fighting has gone on around the town, near the Lebanese border, for weeks.
Opposition groups say militants from the Lebanese Hezbollah movement are fighting alongside government forces.
Correspondents say Qusair has strategic value for both sides. If the government retakes it, it would ensure access from the capital to the coast.
For the rebels, control of Qusair means they can come and go from neighbouring Lebanon, says the BBC's Jim Muir, in Beirut.
Syrian opposition activists said government air strikes and heavy shelling on Sunday had killed at least 30 people in Qusair, including 16 rebel fighters.
State TV said that troops had taken over buildings in the centre, including the town hall, and were now chasing out "terrorists" - its term for rebel fighters.
It said at least 70 rebels had been killed in the advance, but there is no independent confirmation.
Earlier, Rami Abdel Rahman, of UK-based activist group the Syrian Observatory for Human Rights, said troops were advancing from the south and Hezbollah fighters were "playing a central role".
"Soldiers and tanks are trying to advance into the town, the rebel forces are attempting to push them back," he told AFP news agency.
