Government troops and allied militia have recaptured half of the besieged region in a blistering assault launched on Feb 18.
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.
State TV showed 13 bearded men, who it said had earlier handed themselves over to authorities, boarding a bus.
"We were taken aback by the fighting that broke out despite guarantees from the parties involved in this conflict that humanitarians could enter Douma, in eastern Ghouta", said Robert Mardini, regional director for the Red Cross group.
In mid-February, President Bashar al-Assad's government stepped up its assault on the area.
The presence of H.T.S. has been a chief justification cited by the Syrian government and its most powerful ally, Russia, for the scorched-earth bombing campaign they are carrying out in Eastern Ghouta.
Since 18 February, government troops have taken control of half the region, one of the last held by rebels.
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On Friday a United Nations convoy was able to successfully deliver aid to the area, after previous deliveries were halted by shelling. Reaching them would physically cut northern parts of eastern Ghouta from its southern parts. Damascus and Moscow accuse the rebels of preventing people from fleeing the fighting.
Rami Abdurrahman, who heads the Britain-based Syrian Observatory for Human Rights, said Douma was shelled before the convoy went in.
Tens of thousands of people have fled further into the enclave in the face of the warfare, a United Nations official said on Thursday, and residents of Douma said shelters were crowded with the new arrivals.
That has in effect cut the large towns of Harasta and Douma off from each other and the rest of the enclave, it added.
A second attempt was later made to deliver the aid that agencies had failed to offload, but this was cancelled at the last minute due to security concerns.
The renewed artillery fire came as representatives of Damascus and businessmen pressed negotiations on a solution that would allow civilians or fighters to leave the enclave, the Observatory said.
In a surprise move, several members of Syria's armed opposition have been evacuated from rebel-held Eastern Ghouta late on Friday, sources said. They said at least five people were killed in Friday's bombardment of the town of Jisreen.
The World Health Organization said it has verified 67 hits on medical facilities in Syria through January and February, almost half of them in Eastern Ghouta. "This is what makes me so anguished", he said.