Syria war monitor said that President Bashar al-Assad has left the country, after losing swathes of territory to a lightning offensive led by an Islamist-led rebel coalition that said it entered Damascus on Sunday.

Residents in the Syrian capital told AFP heavy gunfire rang out, after a source close to Hezbollah saying fighters from the key Assad ally had left their positions around Damascus.

The president's reported departure comes less than two weeks after the Islamist Hayat Tahrir al-Sham (HTS) group launched its campaign challenging more than five decades of rule by the Assad family.

"Assad left Syria via Damascus international airport before the army security forces left" the facility," Rami Abdel Rahman, head of the Syrian Observatory for Human Rights told AFP. The media was unable to immediately confirm the report.

After saying their forces were heading into the capital, HTS announced an "end of the era of tyranny in the prison of Sednaya" as they broke into the jail which has become a by-word for darkest abuses of the Syrian regime.

The rapid developments in Damascus come only hours after HTS said they had captured the strategic city of Homs, on the way to the capital.

The defence ministry earlier denied that rebels had entered Homs, describing the situation there as "safe and stable".

Homs lies about 140 kilometres (85 miles) north of the capital and was the third major city seized by the rebels who began their advance on November 27, reigniting a years-long war that had become largely dormant.