Regime forces have pounded southern districts of the capital since April 19 to try to expel the Islamic State group from the area, after the jihadists refused to leave under an evacuation deal.

That bombardment intensified on Friday, the Syrian Observatory for Human Rights monitor said, as regime forces advanced against IS inside the districts.

"Army units backed by the air force and artillery have advanced on numerous axes" in southern Damascus, including the district of Hajar al-Aswad, "after breaking through terrorist defences", state news agency SANA said.

The advance "inflicted great human and material losses" on the jihadists, it said.

Syrian state television said the army has seized control of buildings and a "network of trenches and tunnels" from IS in Hajar al-Aswad.

In the adjacent neighbourhood of Qadam, two children were killed in "mortar rounds fired by terrorist groups", it said.

The Observatory said pro-government forces took control of "buildings and streets in Hajar al-Aswad and Qadam after attacking the districts at dawn".

Regime forces were locked in violent clashes with IS fighters on Friday morning, the monitor said.

Heavy air strikes and shelling had targeted Yarmuk and the edges of Hajar al-Aswad and Qadam since the early morning.

IS has held parts of Hajar al-Aswad and Yarmuk since 2015 and seized Qadam last month.

At least 74 regime personnel and 59 IS fighters have been killed in eight days of fighting in southern Damascus, the monitor said.

The latest civilian deaths bring to 36 the number of non-fighters killed in regime bombardment in that same period, it said.

Yarmuk and the surroundings are now IS's largest urban redoubt in Syria or neighbouring Iraq.

The jihadists have lost much of the territory they once controlled in both countries since they declared a cross-border caliphate there in 2014.

Yarmuk was once home to around 160,000 people, but today just a few hundred people remain, the United Nations' agency for Palestinian refugees has said.

President Bashar al-Assad's regime set its sights on the south of the capital after reconquering a major rebel bastion east of Damascus earlier this month.

Eastern Ghouta fell after a blistering air and ground assault and Russia-backed evacuation deals that saw tens of thousands of people bussed out to northern Syria.

More than 350,000 people have been killed and millions displaced since Syria's war started in 2011 with the brutal repression of anti-government protests.