The Syrian Observatory for Human Rights in Britain said it got the information from its activists inside the country, The New York Times reported. It said the victims were found in the basement of a building in Daraya.
The Daraya Coordination Committee said at least eight of the dead were from one family and included a woman and her three children.
Daraya has been under heavy shelling as forces loyal to President Bashar Assad attempt to clear rebels from the capital.
While some Syrian dissidents said the bodies found in Daraya had been shot execution-style, video posted on the Internet suggested some might have been killed by shelling, possibly several days ago, the Times said.
Violence has spread across the border from Syria to Lebanon. This week, 16 people were killed in fighting in Tripoli between supporters of the Syrian rebels and the Assad regime.
But the city appeared calm Saturday, The Daily Star reported.
In neighboring Lebanon, the Shiite Meqdad clan had begun releasing all but four Syrians the clan was holding hostage, a Meqdad leader said.
Meqdad family spokesman Maher Meqdad identified the four remaining hostages as leaders of the rebel Free Syrian Army, The Daily Star reported.
"We have started releasing the Syrians in our custody. We will keep four only," Meqdad told the Star by telephone, explaining that the hostages were being driven home by family members.
The Meqdad clan snatched at least 20 Syrians in response to the mid-August abduction of Hassan Meqdad in Damascus, the newspaper said. The clan blames Hassan Meqdad's abduction on the rebel Free Syrian Army, which has denied holding him.
The family said it also was holding Turkish businessman Aydin Tufan Tekin, who was kidnapped Aug. 15 in Beirut, Lebanon.
2014: The Year in Music [PHOTOS]