Rebels on a lightning advance through Syria yesterday said they have begun to encircle Damascus as government forces denied they had withdrawn from areas near the capital.

"Our forces have begun the final phase of encircling the capital, Damascus," said rebel commander Hassan Abdel Ghani, with the Islamist-led alliance that launched the offensive.

The defence ministry flatly denied the army had fled positions near the city.

"There is no truth to news claiming our armed forces, present in all areas of the Damascus countryside, have withdrawn," it said.

It also said the president is working from Damascus denying reports Assad has left the capital.

Earlier, a war monitor and Abdel Ghani said rebels were within 20 kilometres of Damascus as government forces fell back in the face of the offensive gathering even more momentum.

The Syria Observatory for Human Rights said government forces had ceded more key ground, losing control of all of southern Daraa province and evacuating posts in Quneitra, near the Israel-annexed Golan Heights.

The monitor said government forces were also pulling out of towns as little as 10 kilometres (six miles) from Damascus.

Abdel Ghani said earlier that "our forces were able to control the Saasaa (security) branch in the Damascus countryside. The advance towards the capital continues."

Air strikes and shelling by government forces and their ally Russia killed at least seven civilians near the city of Homs, as the army sought to slow the rebel advance there.

The astounding rebel gains have brought the Islamist group Hayat Tahrir al-Sham (HTS) and its allies to the doorstep of President Bashar al-Assad's seat of power, just over a week into a renewed offensive in a conflict that had long seemed frozen.

As the rebels seize more territory, they have also sought to reassure those living in areas now under their control.

Abdel Ghani in a statement on Telegram Saturday recognised that the rebels had taken areas where "different religious sects and minorities" live.

"We ask that all sects be reassured... for the era of sectarianism and tyranny has gone away forever," he said.

Syria's civil war, which began with Assad's crackdown on democracy protests, has killed more than 500,000 people and forced more than half the population to flee their homes.

The HTS-led alliance has made rapid gains in the West since launching its offensive on November 27.

By Friday, the government was also pulling its troops out of Deir Ezzor in the east, with Kurdish-led forces saying they had moved in.

The HTS leader, known by his nom de guerre Abu Mohammed al-Jolani, said in an interview published Friday the offensive's aim was to oust Assad.

"The goal of the revolution remains the overthrow of this regime. It is our right to use all available means to achieve that goal," he told CNN.