Eastern Ghouta has been besieged since 2013 but a relentless assault over the past three weeks has seen the Syrian army capture half of the territory, and is estimated to have killed almost 1,000 people.
The Syrian government army has made a significant advance in Eastern Ghouta which is the last remaining major rebel-held area near the capital, Damascus.
It showed footage of people getting onto a bus.
The mission followed what opposition activists and a war monitor said was one of the quietest nights in eastern Ghouta since Syrian government forces escalated their assault on the rebellious region on February 18.
The Britain-based Syrian Observatory for Human Rights also said on Saturday that warplanes, helicopters and artillery were used in bombardment of the area overnight.
Syrian President Bashar al-Assad and Russian Federation, his main ally, say the campaign is needed to end rebel shelling of Damascus and to end the rule of rebels over the area's civilians.
The cease-fire endorsed more than a week ago by the United Nations Security Council - but not yet implemented - does not cover H.T.S., a coalition of rebel forces led by the Nusra Front, a group that was formed as Al Qaeda's Syria affiliate and is listed internationally as a terrorist group.
The two largest groups are Jaish al-Islam and its rival Faylaq al-Rahman.
Mekdad also pointed out that the Syrian government had asked global investigators to investigate reports about a chemical incident in Khan Sheikhoun but the request was declined over alleged poor security conditions.
In a statement published on Twitter on Friday, the group said the decision had been made in consultation with the United Nations, a number of worldwide parties and civil society representatives from eastern Ghouta.
Air strikes started up again after the evacuation, killing nine people and injuring around 28, the Observatory said. Another man said there were 15 families in the basement who have been hiding for days.
Insurgent groups in eastern Ghouta deny this, but a Reuters witness on Friday saw gunfire and mortar fire from inside the rebel territory near one of the crossing points.
The channel has been reporting since last week that rebels have prevented civilians from leaving. It accused the government of using "poison gas".
However, the terror of the bombardment and the desperate living conditions are taking their toll and may push people to courageous the fighting and flee.
More than a dozen fighters and their families evacuated from Eastern Ghouta and brought to Idlib, state media reports.
"The bomb shelters and basements are full, and people are sleeping in the streets and in public gardens", the statement said.