The two largest groups are Jaish al-Islam and its rival Faylaq al-Rahman.
Mohammad Alloush, one of Jaish al-Islam's leaders, told pan-Arab television channel al-Arabiya al-Hadath on Friday that there are no more than "a few hundred" Nusra fighters in Eastern Ghouta, Reuters reported.
"The bomb shelters and basements are full, and people are sleeping in the streets and in public gardens", the statement said.
The food parcels were supposed to be delivered on Monday when another aid convoy entered Douma, but the fighting and bombardment then forced it to leave early without unloading all its supplies.
The aid was delivered with helicopters hovering overhead and warplanes targeting areas outside Douma, a correspondent in the town said.
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.
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At the venue of FC Porto, Liverpool got a big victory over them where Sadio Mane scored an fantastic hat trick. They are all good teams [left in the draw], but I don't think it matters to us.
Doctors and nurses in the beleaguered enclave have run out of several life-saving items and a massive medical re-supply is critically urgent, Doctors Without Borders (MSF) said Friday.
The UN convoy was the first to reach the some 400,000 residents of Eastern Ghouta since the government began its offensive there in mid-February. Any solution to the crisis will probably involve a partial evacuation of rebel fighters and perhaps civilians, in a deal similar to past surrender agreements between the government and rebels. "We want to save our children and all those who have not died", said Abu Riyadh, a 47-year-old man in the town.
A tribal leader said more than 300 civilians from the areas of Kafr Batna, Saqba and Hammuriyeh wanted to leave.
The ferocious three-week assault on the last major rebel stronghold near Damascus has captured about half its area and killed 960 people, according to a war monitor.
The UN secretary general has described the situation in eastern Ghouta as "hell on earth" and the body's high commissioner for human rights described the military offensive as a "monstrous annihilation".
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.