BEIRUT -- Islamic State fighters on Sunday pushed into a large district in southern Damascus, clashing with rival militants just a few kilometres from the centre of the Syrian capital, the extremist group and Syrian activists said.

More than two dozen militants were killed in the clashes on the edges of the Qadam neighbourhood, said the Britain-based Syrian Observatory for Human Rights, which has an extensive network of activists on the ground.

The pro-IS Aamaq News Agency reported that IS fighters seized half of Qadam. The Observatory's Rami Abdurrahman said IS fighters were holding two streets and that fighting was continuing.

IS supporters posted propaganda pictures claiming to show IS fighters advancing in the narrow streets of Qadam. The authenticity of the images could not be confirmed independently.

IS has emerged as one of the most powerful forces in the battle to overthrow Syrian President Bashar Assad. The extremist group has seized about one-third of Syria and neighbouring Iraq over the past year.

Armed Islamic factions fighting forces loyal to Assad control parts of the Syrian capital and large parts of the city's suburbs. Earlier this year, IS fighters entered the Palestinian refugee camp of Yarmouk, east of Qadam, and control large parts of it.

Also Sunday, a mortar round hit an upscale neighbourhood of central Damascus, killing four people, including a girl, Syrian state TV said.

It is not uncommon for Damascus to be shelled. Sunday's attack targeted the posh neighbourhood of Abu Rummaneh, which houses hotels and several embassies.

An Associated Press reporter on the scene saw two people wounded by shrapnel. Vehicles in the area were also damaged.

Associated Press writer Albert Aji in Damascus, Syria contributed to this report.