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Heavy regime bombardment pounded a southern district of Syria's capital on Saturday, state media and a monitor said, as government forces pressed their campaign against Islamic State jihadists entrenched in the area.

IS still holds large parts of the Palestinian refugee camp of Yarmouk and the adjacent Hajar al-Aswad and Tadamun districts on the southern edge of Damascus.

Since Thursday, regime forces have been shelling them heavily in a bid to pressure IS fighters to withdraw.

The Syrian Observatory for Human Rights, a Britain-based war monitor, said six civilians have since been killed.

"There are clashes and intense air strikes today, but no strategic advance on the ground," Observatory head Rami Abdel Rahman told AFP.

Syrian state news agency SANA said government forces were targeting IS supply lines and had destroyed weapons depots in the area.

A reporter contributing to AFP from inside Yarmuk said there was steady shelling throughout the day on Saturday, with the booms of air strikes reverberating across the district.

Residents were hiding in the basements or ground floors of their modest cinderblock homes, too afraid to go outside.

Syrian warplanes and helicopter gunships could be seen flying above the camp, as billowing masses of thick grey smoke emerged from the skyline.

Once a thriving district home to some 160,000 Syrians and Palestinians, Yarmuk has been devastated by more than five years of clashes and a crippling government siege.

Thousands have fled over the years as the humanitarian situation has grown more dire.

IS overran most of Yarmuk in 2015 and al-Qaeda's former Syrian affiliate maintained a small presence in Yarmuk until it withdrew a few weeks ago.

Another small pocket is controlled by the regime and allied Palestinian fighters.

IS overran large swathes of Syria and neighbouring Iraq in 2014, but has since lost most of that territory to several offensives.