Syria's president, Bashar Assad, lost control of large sections of the country in the early years of the war, which began in 2011, and seemed headed for defeat before Russian Federation intervened on his behalf in 2015.
The government has denied reaching a deal with IS.
Syrian president Bashar Assad meets Vladimir Putin for talks in Sochi on May 17 Credit MIKHAIL KLIMENTYEV AFP
One military source close to the regime said fighters had left under a deal reached through negotiations with the government and its ally Russian Federation. The Observatory said the month of fighting left scores of dead on both sides.
The army made the announcement in a televised statement after establishing control of the Damascus neighborhood of al-Hajar al-Aswad on Monday, according to local media.
According to the Syrian official news agency SANA on Sunday, combat tactics aimed at cleansing building blocks, tunnels and trenches, and fortified points of the lingering presence are now being used in the region located to the south of the capital city Damascus.
The Syrian Observatory for Human Rights, a United Kingdom -based war monitor group, said there was a Russian-brokered deal between the Syrian government and IS militants to leave the area.More news: Taylor Swift and Hailey Baldwin suffer wardrobe malfunctions at Billboard Awards
The Observatory said Monday that a new batch of fighters and their families left late Sunday, heading east toward the Syrian desert. The Observatory said IS militants began burning their posts in Yarmouk and adjacent areas.
More than 1,000 Islamist fighters and civilians left Qadam in March for opposition territory in northern Syria.
The UN says 110,000 people have been evacuated to northwestern Syrian and rebel-held areas north of Aleppo.
The opposition has called it a policy of forced displacement amounting to demographic change to drive out Assad's opponents.More news: Pence warns Kim not to 'play' Trump
For proponents of the Syrian government, Monday was a day for celebration.
While Assad has vowed to win back "every inch" of Syria, the map of the conflict suggests a more complicated time ahead from now on.
The U.S. military is in much of the east and northeast, which is controlled by Kurdish groups that want autonomy from Damascus.
Iranian-backed militias, including the Lebanese group Hezbollah, have been instrumental in helping Assad's over-stretched forces recapture huge areas around Damascus and in the country's centre and north, building a military presence that has alarmed Israel and its USA ally, which is now looking to constrain Iran's activities.More news: Cougar kills mountain biker and injures another in Washington state