Activists in the town, along the Lebanese border, said Sunday that security forces intensified their assault during the day, hitting Qusair with artillery and warplanes and destroying multiple homes.
The Britain-based Syrian Observatory for Human Rights said at least 52 people were killed, including 48 rebel fighters.
A Syrian official told Western news agencies that government troops had captured the municipal headquarters and surrounding buildings. Syrian state television said security forces then began hunting down terrorists - the government's term for rebels fighting a two-year war to oust President Bashar al-Assad.
There was no independent confirmation.
One of the Islamist units defending Qusair (the al-Siddiq Brigade) said attempts to storm the town had failed. Another activist in the Qusair region said the rebel grip was tenuous but that the army was not in control.
Syrian troops had cut off Qusair on three sides and captured surrounding villages in recent weeks. The town lies near a highway from Damascus to the Syrian coast and controlling it would solidify President Assad's access to coastal regions largely inhabited by his minority Alawite sect.
Qusair also has formed part of a cross-border smuggling route for rebels.
Meanwhile, as Syrian refugees continue to stream into Jordan and Lebanon, the international aid group Oxfam warned that warmer summer weather will increase health-related risks due to a lack of shelter, water and basic sanitation.
Increased cases of public health-related diseases such as diarrhea and skin infections have already been recorded in host communities and temporary settlements, where an increasing number of refugees now live.
In Lebanon's Bekaa Valley alone, there are now some 240 tented settlements, six times the number recorded in January.
As of May 2013, some 635,000 people are in need of assistance in Lebanon - both refugees and host communities - and Oxfam says it anticipates this number to increase to over 740,000 by November.
More than 80,000 people have been killed and several million displaced since the start of the rebellion against Assad in March 2011.
Some information for this report was provided by AP,AFP and Reuters.
Syrian Troops, Hezbollah Attack Rebel-Held Qusair
Syrian government troops backed by warplanes and Lebanese Hezbollah militants have attacked the rebel-held town of Qusair, as part of a weeks-long offensive to recapture the strategic area connecting Damascus to the Mediterranean coast.