The source said that army units continued operations against the gatherings and hotbeds of terrorist organizations at the southern outskirts of Damascus, seizing control of al-Mazniyeh, al-Qadam, al-Asali, and al-Joura neighborhoods after destroying the terrorists' fortified positions and inflicting heavy losses upon them in personnel and weaponry.
The monitor, the Syrian Observatory for Human Rights, said it had gained control of several buildings in the densely built-up area.
The announcement comes at the tail of a regime offensive in the city including the Palestinian refugee camp Yarmouk.
Syrian soldiers patrol in al-Joura neighborhood after it was recaptured from Islamic State militants.
On Sunday, government war planes pounded Yarmouk and the neighbouring district of Hajar al-Aswad, it said.More news: Ronaldo warns Messi not to celebrate Barcelona's La Liga title triumph
The Syrian army reached a deal with opposition fighters to evacuate the areas of Yalda, Babila and Beit Sahem, near the site of a government offensive against militants, south of Damascus on Sunday.
The reported deal is the latest in a string of such agreements that have seen the regime retake areas near the capital after rebel withdrawals.
The militants have held parts of Yarmouk and Hajar al-Aswad since 2015, and overran Qadam in a surprise assault last month.
Regime forces were locked in violent clashes with IS fighters on Friday morning, the Britain-based monitor said.
Yarmuk and the surroundings are now IS's largest urban redoubt in Syria or neighbouring Iraq.More news: Israel's live fire use against Gaza protesters challenged in court
At least 85 government fighters and 74 IS militants have been killed in 10 days of fighting in southern Damascus, the Observatory said.
Since the beginning of the campaign on April 19, at least 18 civilians have been killed, activists in nearby rebel-held towns said.
The Palestinian refugee population of Yarmouk had dwindled from around 160,000 in 2011 to just 6,000 last month, according to United Nations estimates.
President Bashar Assad's regime set its sights on the south of the capital after reconquering a major rebel bastion east of Damascus earlier this month.
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Before the outbreak of the Syrian civil war in 2011, Yarmouk was home to around 160,000 Palestinian refugees - people who had been displaced from their homes in modern-day Israel during the 1948 war, and their descendants.