Eastern Ghouta is the last remaining opposition-controlled zone on the outskirts of the capital, and rebels there have regularly fired rockets onto Damascus.
The two largest rebel groups in the area, Jaish al-Islam and Failaq al-Rahman, have yet to comment on the report, Reuters stated today.
The government forces advanced from the east and were now almost a mile away from forces on the western side of eastern Ghouta, cutting links between the rebels in northern and southern parts of the suburb.
It is hard for aid convoys to reach eastern Ghouta and the global community is failing to intervene.
Syrian President Bashar al-Assad and Russian Federation, his main ally, said the campaign was needed to end rebel shelling of Damascus and to end the rule of Islamist insurgents over the area's civilians.
Takfiri groups in eastern Ghouta deny this, but eyewitnesses on Friday saw gunfire and mortar fire from inside the rebel territory near one of the crossing points.
The Observatory reported that troops are advancing under the cover of attacks by warplanes and helicopter gunships and confirmed that government forces captured large parts of Misraba.
Syrian state television aired footage of a single bus carrying 13 "fighters" and family members out of the enclave through Al-Wafideen checkpoint, without giving their affiliation.
But since entering into force late last month, no major evacuation took place in Eastern Ghouta, with the Syrian government accusing the rebels of targeting the civilians who are attempting to leave.
The government says its forces now control half the enclave.
An estimated 950 civilians have been killed in the Eastern Ghouta region since the Russian-backed government assault was launched on 18 February, according to the UK-based Syrian Observatory for Human Rights (SOHR) monitoring group, which has a network of sources on the ground.
According to the report, the government of Syrian President Bashar Assad is responsible for the use of sarin in the Khan Sheikhoun incident, while Daesh* is responsible for the use of sulfur mustard in Umm Hawsh.
It said the initiative was "based on consultations between Jaish al-Islam and the United Nations, and a number of global actors".
Hundreds of thousands of residents are still thought to live in the Eastern Ghouta, seven years into the civil war.
The two insurgents said earlier that they had staged counter-attacks in recent days that retook some lost positions.
The four civilians were trying to pass through a recently opened humanitarian corridor from Jisrein to Mlekha during the twelfth humanitarian pause, SANA reported citing its journalist on the ground on Saturday.