State media said the army “restored security and stability” to most of the town – a claim denied by activists.
Lebanese militants are said to be involved – Hezbollah siding with the army, Sunni gunmen with the rebels.
More than 50 people have reportedly been killed. The fighting has also spilled into Lebanon.
Several mortar rounds fired from Syria struck Lebanon’s north-eastern town of Hermel, Lebanon’s National News Agency said, but no casualties or major damage were reported.
It said that in the northern Lebanese city of Tripoli, at least five people were injured in clashes between supporters of Syrian President Bashar al-Assad and rebel backers.
In a separate development, the UK-based Oxfam aid agency warned that Jordan and Lebanon were in urgent need of help to support hundreds of thousands of Syrian refugees who had fled the fighting.
Oxfam said a combination of rising summer temperatures and poor sanitation posed increased health risks for the refugees. More than 100 cases of a condition known as “Aleppo boil” had been diagnosed in Lebanon in the past two weeks, caused by a parasite, it added.
Syrian troops on Sunday managed to secure most of Qusair and “eliminated large numbers of terrorists, most of them non-Syrians”, the state-run Sana news agency reported.
It quoted a military source as saying that dozens of rebels had surrendered and the army was now “pursuing the armed terrorist groups in some areas” of the town.
Qusair resident and opposition activist Hadi Abdullah said government troops were engaging in house-to-house battles on Sunday, according to the Associated Press.
“It’s the heaviest [shelling] since the beginning of the revolution,” he said, quoted by AP news agency.
He also denied the regime had made advances in the town.
UK-based activist group the Syrian Observatory for Human Rights said that 52 people were killed in Qusair: 48 fighters and three civilians.
Unconfirmed reports in Lebanese media said that a number of Hezbollah fighters had been killed in a rebel ambush.
The town – close to the border with Lebanon and with a population of 30,000 – has great strategic value. Its control would give the government access from the capital to the coast.
For the rebels, control of Qusair means they can come and go from Lebanon.
In recent weeks the Syrian military has won back surrounding villages and countryside and has encircled Qusair in Homs province.
Earlier this month, Syrian forces reportedly dropped leaflets on the town, warning that it would come under attack if opposition forces failed to surrender.
The UN said last week that the death toll in Syria had reached at least 80,000 since the conflict began in March 2011.
Activists said the number could be as high as 120,000.
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