They have also been forced out of Yalda and Beit Sahem, in the capital, according to the Syrian Observatory for Human Rights.
Syrian rebels battled militants from the Islamic State (IS) near Damascus on Monday, pressing their bid to expel them from their strongholds, a monitoring group said.
Rebels holding positions in southern Damascus and the outskirts of the capital and seeking President Bashar Al Assad’s ouster, launched an offensive some three weeks ago to expel IS.
IS was initially welcomed by some rebels as a potential ally in the armed revolt, but the opposition, including Islamists, has turned against it.
IS fighters have in recent days been expelled from the towns of Mesraba and Maydaa, in the Eastern Ghouta area east of Damascus.
They have also been forced out of Yalda and Beit Sahem, in the capital, according to the Syrian Observatory for Human Rights.
The expelled militants fled to Al Hajar Al Aswad, Tadamon and Qadam in southern Damascus, “where they have a strong presence”, said Observatory director Rami Abdel Rahman.
Then, at dawn on Monday, fighting broke out in the battered neighbourhoods of Al Hajar Al Aswad and Qadam, pitting rebels against IS militants, Abdel Rahman said.
“The rebels want to expel IS from the Damascus area,” he added.
IS controls much of eastern Syria, and it has its main stronghold in Raqa, in the north of the war-torn country.