A US-led military coalition fighting Daesh in Syria and Iraq said in an emailed statement to Reuters it was "aware of reports of an evacuation near Yarmouk and south Damascus" and was monitoring the situation.
The recapture of IS-held pockets in the Palestinian refugee camp of Yarmuk and the nearby Hajar al-Aswad district in southern Damascus on May 21 came after a massive bombing campaign that decimated the remains of the residential area where about 200,000 Palestinian refugees used to live.
Last year, IS fighters and relatives were evacuated from an area on the Lebanese-Syrian border under a deal between IS and Hezbollah, the regime's powerful Lebanese ally.
Located eight kilometers south of Damascus and inhabited mostly by Palestinian refugees, the Yarmouk camp sits on 16 square kilometers of land.
In December 2016, government forces captured rebel-held eastern neighbourhoods of the northern city of Aleppo, in Assad's biggest victory since the conflict began.
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With a mix of military pressure and surrender deals brokered by Russian Federation, thousands of opposition fighters capitulated and were evacuated in March and April from Damascus suburbs known as eastern Ghouta after a crushing government offensive.
With a blend of military pressure and negotiated withdrawals, Syrian President Bashar al-Assad has flushed rebels out of key territory around Damascus in recent months, leaving a last pocket of IS fighters in the capital's south.
The first group of ISIS fighters was transferred by bus out of southern Damascus on Sunday, the monitor said.
The state TV aired footages of the largely-devastated Hajar al-Aswad with Syrian soldiers firing celebratory gunshots while chanting for the Syrian army. It added that IS fighters have been setting their offices and vehicles on fire so that government forces would not be able to seize equipment or documents belonging to the group.
"As a result of a joint operation of our armed forces and allies, Al Hajar Al Aswad and the surrounding territories have been completely liberated from terrorists", the army said in a statement.
Russian Federation and Iran have been Assad's strongest backers and have joined the war on his side.
Mr. Putin told Mr. Assad during a meeting on Thursday that a political settlement in Syria should encourage foreign countries to pull out their troops from Syria.