"A group of critical medical cases will be evacuated with those accompanying them via the Wafideeen" checkpoint into government-held territory, the head of Jaish al-Islam's political office, Yasser Delwan, said.
The Al-Wafideen crossing is one of two humanitarian corridors that the Syrian government has set up in coordination with Russian Federation.
While appeals for all parties to adhere to a United Nations resolution demanding a ceasefire have fallen on deaf ears, for the first time on Tuesday a total of 35 people in need of urgent medical treatment and their chaperones were escorted out of the area safely.
Russian Federation and Syria have set up safe corridors for civilians to leave Eastern Ghouta, but militants holed up in the region have been shelling the safe routes to block the evacuation process.
The expulsion of the rebels from eastern Ghouta would represent their biggest defeat since they lost their enclave in Aleppo in December 2016.
Eastern Ghouta's 400,000 residents have been living under government siege since 2013, facing severe shortages of food and medicines shortages even before the latest assault.
"It is not the path we prefer, but it is a path we have demonstrated we will take and we are prepared to take again", Haley said.
On Monday, Syrian government troops discovered, during a mopping-up operation in a village in Eastern Ghouta, another secret workshop constructed for production of various chemical munitions.
Samya Jaber, another evacuee who managed to leave Eastern Ghouta with her father and three children, said she was desperate to have her critically ill father get access to medication.
It said in the last quarter of 2017, more than a million people fled their homes, with a 60% increase since the announcement of the creation of the de-escalation zones. Damascus wants to gain territory, with the help of Russian Federation, to secure its interests during peace talks.
"Right now we're getting reports - I don't have evidence that I can show you - but I'm aware of the reports of chlorine gas use", he said before arriving Sunday in Oman. French President Emmanuel Macron has warned the Syrian regime that the use of chemical weapons will result in French retaliation, but the Syrian government claims it has never used this kind of munition.
A Syrian soldier walks toward an armored vehicle in the town of Aftaris in Damascus' Eastern Ghouta countryside, Syria, on March 12, 2018.
Syria has only just begun to emerge from a devastating conflict that began in early 2011 when the Bashar al-Assad regime cracked down on demonstrators with unexpected ferocity. The situation in the city, which has already been suffering from the years of besiegement and, therefore, a lack of food, clean water and medical supplies, has gone from bad to worse. A lot of people can not afford that anymore. "It is much more hard in eastern Ghouta because we have to negotiate with the Syrian regime and are at the mercy of its decisions", Mylius told DW.
U.N. Secretary-General António Guterres noted during the council meeting that "there has been no cessation of hostilities" in Syria, as "violence continues in eastern Ghouta and beyond - including in Afrin, parts of Idlib and into Damascus and its suburbs".