The so-called Syrian Observatory for Human Rights, which claims to be a monitoring group opposed to the Syrian government, made the report. The state news agency SANA, however, did not give a death toll for the ambush, but said the rebels were from the al-Qaeda-linked al-Nusra Front.
According to the report, all the militants were killed and machineguns and rocket-propelled grenades confiscated.
SANA said the terrorists included non-Syrians and the Observatory said that eight militants were still unaccounted for after the attack, which happened west of an industrial area east of Adra.
The Syrian armed forces have been on the offensive around Damascus after the militants pushed into towns and suburbs on the outskirts of the capital last year. Adra is in the East Ghouta region, which has been besieged by the army for months.
The army has made efforts to secure the capital and its links to the western coast while the militants have overrun much of the north and east.
The war in Syria started in March 2011, when pro-reform protests turned into a massive insurgency following the intervention of Western and regional states.
More than 100,000 people have died in the foreign-hatched civil war and millions have been displaced.