The British-based Syrian Observatory for Human Rights said the death toll could rise to 80 in what it called a new massacre.
Photogrraphs posted online by activists showed the bodies of about a dozen men lying by a river in the Bustan al Qasr neighbourhood.
Meanwhile, more than 700,000 Syrian refugees have registered in neighbouring countries or await processing there, and aid workers are struggling to keep up with the exodus.
A UN spokeswoman said: "We have seen an unrelenting flow of refugees. We are running double shifts."