Almost 400,000 people have been trapped in Eastern Ghouta since 2013 when insurgents first took over control and the government began its offensive to oust the rebels.
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.
"It has been agreed that the first group of HTS members be released from the prisons of Jaish al-Islam".
Media playback is unsupported on your device Media captionAfrin What is going on in Syria's other battle
The Russian military has repeatedly said that terrorists use civilians as human shields and their homes as shelters.
Earlier, 13 trucks loaded with 2,400 food parcels crossed into Eastern Ghouta, the International Committee of the Red Cross said, entering what United Nations chief Antonio Guterres has called "hell on earth".
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. It is hard for aid convoys to reach eastern Ghouta and the global community is failing to intervene.More news: Derrick Rose has agreed to sign with Timberwolves, AP source says
The International Committee of the Red Cross said the aid convoy passed through front lines and was heading to the enclave's biggest town, Douma.
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.
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. "None of the civilians has been able to leave the enclave over the last 24 hours", Yevtushenko said.More news: New Orleans Pelicans vs. Washington Wizards - 3/9/18 NBA Pick, Odds, and Prediction
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.
UN High Commissioner for Refugees Filippo Grandi on Friday called the conflict a "colossal human tragedy".
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.More news: Saudi Grants Airspace Approval For Flights To Israel
Saturday, Ankara-backed rebels advanced against Kurdish militia in northwest Syria, coming to within two kilometres (just over one mile) of the flashpoint town of Afrin, the Observatory said.
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