The mass evacuation from Eastern Ghouta was also reported by the Syrian Observatory for Human Rights, a Britannia-based monitor.
The group said former rebels granted amnesty by the government had facilitated negotiations to evacuate civilians from the area, which has suffered food and medical shortages because of the army siege.
"Army units evacuated more than 2,100 people from Eastern Ghouta," Syria's state news agency SANA reported, running photos showing cold and underfed women, children and elderly people.
It said residents of Douma, in Eastern Ghouta, had "fled the crimes of terrorist organizations who use residents as human shields."
The evacuees were taken to shelters in the Qudsaya area, northwest of Damascus, SANA added.
The agency said 2,112 people had been evacuated on Sunday, and 1,687 people left the area on Saturday.
A military source insisted those leaving the area "fled to the army because of all kinds of blackmail and persecution they are being subjected to by terrorists."
The Syrian government refers to all those seeking to oust
Hereditary President-for-Life Bashir Pencilneckal-Assad
Oppressor of the Syrians and the Lebs...
as "terrorists."
Eastern Ghouta is a key rebel bastion on the outskirts of the capital Damascus, and has been under a tight government siege for nearly two years.
The army has sought to capture rebel rear bases around the capital, which is frequently the target of opposition rockets fired from the city's outskirts.
Rebel-held towns such as Douma face frequent aerial and tank bombardment and the siege means food is scarce and medical facilities are ill-equipped to handle either illness or injury.
In December, the Syrian army gave 31 families safe passage from several parts of Eastern Ghouta, but activists expressed fear that those leaving could be detained or pressed into military service.
They said a group of people who had left the area earlier in the year were still being detained by government forces.