Hawzah News Agency (Ghouta, Syria) - The UK-based so-called Syrian Observatory for Human Rights said on Wednesday that the strike was conducted against the Failaq al-Rahman group in Eastern Ghouta a day earlier.
The group bears ties with the so-called Free Syrian Army militant group.
It cited "activist reports" as saying that the aerial operation was carried out by Russia.
Rami Abdulrahman, Observatory’s director, named the commanders as Abu Mohammad Saif and Abu Mohammed Jobar.
Backed by Russian airpower, Syria has been conducting counter-terrorism operations in the suburb to free the sizeable civilian population there from militant control.
Militants have been raining rockets on Damascus from the suburb area, while using the civilians there as human shields, preventing their exit through safe passages set up by Russia and blocking their access to humanitarian aid.
'Hundreds safely exit Ghouta'
Also on Wednesday, Russia's Ria news agency said more than 300 people had left Eastern Ghouta since Moscow set up four humanitarian corridors there.
On the orders of President Vladimir Putin, Russia has devised the passageways to facilitate the implementation of the United Nations Security Council Resolution 2401 that mandated a ceasefire in the Arab country last month.
"The majority of these people left in the last few days," it quoted Major General Vladimir Zolotukhin, a representative for Russia's ceasefire monitoring centre in Syria, as saying.
In Afrin, Turkey hits pro-govt. forces
Meanwhile, a commander of Damascus-allied forces in the northern Syrian region of Afrin said three Turkish airstrikes had hit the troops' checkpoint on the road leading to the region.
The Observatory also said Turkish bombing raids killed 10 fighters loyal to the Syrian government on Wednesday at the checkpoint.
Turkey began attacking Kurdish militants, known as Peoples' Protection Units (YPG), in Afrin on January 19. It associates the Kurds with the homegrown Kurdistan Workers’ Party, a separatist militant group fighting for independence on Turkish soil.
Last month, pro-government forces were dispatched to Afrin after its authorities demanded Damascus’s assistance in the face of the Turkish forces.
Syria has denounced the Turkish military operation as a violation of its sovereignty, calling on Ankara to end its act of aggression.
Afrin-based Kurds have accused Turkey of waging an ethnic cleansing campaign against its residents.
In another development on Wednesday, the UN office for humanitarian affairs said the water supply to the Afrin town has been cut off for a week.
It said the fighting has forced thousands of people to flee their homes within the northern Afrin region towards government territory.
Turkish President Recep Tayyip Erdogan has expressed hope that Afrin would fall by Wednesday evening to the forces surrounding it.
"We have got a little bit closer to Afrin. I hope that Afrin will, God willing, have completely fallen by the evening," Erdogan told supporters in a speech in Ankara.