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.
Syrian President Bashar al-Assad's forces have besieged Eastern Ghouta since 2013. "So Ghouta will gain by finishing with these people".
On Saturday, at least one child was killed and four other civilians wounded in rebel shelling on eastern districts of Damascus, according to state news agency SANA.
A second convoy with desperately needed aid for the besieged rebel-held eastern suburbs of Damascus was postponed on Thursday because of the violence and a rapidly evolving situation on the ground, the International Committee of the Red Cross said.
Grandi added that while most of the Syrian refugees in Lebanon have expressed a desire to return to their home country, "almost all of them say not right now" and any plans of them returning are "very premature".
Such evacuation deals have been repeatedly agreed in Syria's seven-year war, most notably in the second city of Aleppo in late 2016. "The bombing eased for a bit and is no longer intense", said Bilal Abu Salah, a resident of Douma, before the resumption of air strikes.
A convoy was unable to finish unloading on Monday because of continued fighting, bringing in the remaining undelivered food parcels on Friday despite bombardment nearby.
These involve rebels surrendering territory in exchange for safe passage to opposition areas in northwest Syria, along with their families and other civilians who do not want to come back under Assad's rule.
MSF said doctors inside the enclave were exhausted.
Russia's military has said it is playing a key role supporting the assault on eastern Ghouta to combat "terrorists" hiding there and threatening Damascus.
The military gains have caused wide-scale internal displacement as civilians flee government advances toward areas in the territory still held by the rebels.
The council is to meet on Monday to hear a report from UN Secretary General Antonio Guterres and try to plod on with a bid to turn the ceasefire voted in NY into a reality on the ground.