But the Syrian Observatory for Human Rights, a UK-based monitoring group, says they were wounded rebels and civilians, not active Jaysh al-Islam fighters.
On Friday, opposition activists said 40 people were killed in Douma while state media said four were killed in government-held Damascus.
Douma is the last rebel-held area in Eastern Ghouta, after other towns in the sprawling countryside have seen the evacuation of 43,000 rebels and their families toward Idlib Province in northwestern Syria.
The regime and its ally Russian Federation launched a blistering air and ground offensive on Eastern Ghouta in mid-February, killing more than 1,600 civilians and causing an global outcry.
A commander in a regional alliance that fights for the Assad government said Jaish al-Islam had been offered safe transport out of Douma to rebel-held areas near Aleppo, in the northeast.
Syria's state news agency SANA said Syrian air strikes hit the town in response to rebel shelling onto the capital from Douma.
The pro-rebel watchdog group said intense battles are raging between the Islam Army and the Syrian government forces, with heavy shelling from the Syrian forces and the Russians on Douma.
Barzeh is close to the eastern Damascus suburb of Harasta that opposition fighters evacuated last month following weeks of a crushing government offensive on eastern Ghouta.
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In northern Syria, the Turkish military said on its Twitter account that it has established the ninth observation post in the rebel-held province of Idlib as part of the de-escalation agreement with Russian Federation and Iran.
"It feels like we're back in the days of the Gaza war" when Israel was bombing the Palestinian enclave and people around the world watched, he said, giving his name only as Mohammed.
Several thousand people left Douma in recent days, taken by bus to the rebel-held northern town of Jarablus, which is next to the Turkish border.
For a week the bombardment had subsided as Moscow pursued peace talks with Jaish al-Islam, but talks came to an abrupt halt and air strikes suddenly resumed on Friday afternoon, killing dozens of civilians.
It remains unclear exactly why the talks between Moscow and Jaish al-Islam have faltered.
Speaking on Friday, Stephane Dujarric, spokesperson for the United Nations, said the renewed outbreak of fighting in Douma "is of great concern to us". Residents said Jaish al-Islam has kept a tight hold over the evacuation, requiring those who want to leave to register at local offices.
The group appears to have little leverage, however, to face the regime's recovered might, and the latest strikes raised fears of a brutal end to the five-year-old siege of Eastern Ghouta.