But the group represents only a small portion of the insurgent presence in the enclave, and both Jaish al-Islam and Failaq al-Rahman have said they would not negotiate a similar deal for themselves.
It said the initiative was "based on consultations between Jaish al-Islam and the United Nations, and a number of worldwide actors".
But soon after the convoy of 13 trucks carrying food parcels crossed into Eastern Ghouta, the Observatory and a witness in Douma said air strikes had resumed.
The Syrian government denied the accusations, saying it is the rebels who mounted the attack to frame the government and draw in a military action from the United States.
The aid was delivered with helicopters hovering overhead and warplanes targeting areas outside Douma, a correspondent in the town said.
A picture from Syrian state TV showing unidentified "fighters", evacuated from Eastern Ghouta. "It has been agreed that they be moved to Idlib at their request", Jaish al-Islam said.
Doctors and nurses in the enclave have run out of several life-saving items, according to Doctors Without Borders (MSF), which reported a "terrible medical catastrophe".
On February 24, the UN Security Council unanimously adopted Resolution 2401, which calls for a month-long ceasefire in Syria - especially eastern Ghouta - to allow the delivery of humanitarian aid.
Manafort Pleads Not Guilty to Tax and Fraud Charges in Virginia Court
Ellis also imposed stricter conditions of home confinement then those ordered by U.S. He already has filed a civil suit in the District, making the same argument.
Since then they have reportedly taken control of half of the region, in an advance that is thought to have left more than 900 civilians dead.
"We have no guarantees that the regime will protect the families that want to leave and that it won't send the men to the frontlines", he added.
Damascus and Moscow accuse the insurgents of shooting at civilians to prevent them fleeing the fighting into government areas.
A tribal leader said more than 300 civilians from the areas of Kafr Batna, Saqba and Hammuriyeh wanted to leave.
According to reports, more than 400,000 people still reside in the region, seven years into the Syrian civil war.
In rebel fire on Friday, a woman and a child were killed by a mortar round that hit the Damascus suburb of Jaramana, SANA said.
For President Bashar al-Assad, it would mark a significant victory as he builds on the military momentum created by Russia's entry into the war in 2015 that has restored his rule over large swathes of the country.