"Leaflets were dropped over Qusayr asking civilians to leave the city, with a map of a safe route by which to evacuate, because the attack against the city is coming soon if the rebels do not surrender," the source told AFP on condition of anonymity.
Activist Hadi al-Abdullah, who spoke to AFP over the Internet, denied the claim
"I am in the town of Qusayr, and this morning I visited two villages nearby, and I can assure you no leaflets were dropped anywhere near here," he said.
"What is more worrying than that is that there is no safe exit for civilians. All of us here in Qusayr have been condemned by the regime to a slow death," added Abdullah, a spokesman for the Syrian Revolution General Commission, a network of anti-regime activists.
"Every time civilians try to leave the town, they are shot or shelled at the town's edges by tanks or snipers. We are trapped civilians, activists and fighters together."
Troops backed by fighters from the Lebanese Shiite militant group Hezbollah have advanced throughout the area around Qusayr, which fell to the rebels more than a year ago.
Activists said Qusayr is surrounded by government forces on three sides, and that approximately 25,000 residents are believed to still be in the city.
The area has been a strategic boon to the rebels, who used it as a base from which to block the main road from Damascus to the coast, impeding military movement and supply chains.
It is also important because of its proximity to Lebanon.
The regime has made recapturing it a key objective. President Bashar al-Assad reportedly said last month that fighting in the area was the "main battle" his troops were waging.
Activists say regime forces there are backed by fighters from Hezbollah, as well as members of the National Defence Force, a pro-regime militia.
Meanwhile, the Syrian Observatory for Human Rights watchdog said at least 72 people were killed throughout the country in violence on Thursday, including 33 rebels, 21 civilians and 18 soldiers.