Syrian forces on Sunday advanced toward the strategic town, which is located on the border with Lebanon.
The army says Syrian troops have started entering the town from every front, following weeks of battle.
Clashes have been reported between Syrian forces and militants in several districts across Qusayr. The army says it is making gains in its efforts to clear the area of terrorists.
The strategic town, which connects the capital city of Damascus to the Mediterranean coast, has been the focus of fierce clashes in recent weeks.
Heavy fighting has also been reported in an eastern suburb of the capital. A number of militants have been killed in the clashes.
Unrest erupted in Syria over two years ago. Many people, including large numbers of Syrian soldiers and security personnel, have been killed in the violence.
The Syrian government says that the chaos in the country is being orchestrated from outside, and there are reports that a very large number of the militants are foreign nationals.
In addition, several international human rights organizations say the militants have committed war crimes in Syria.