The Britain-based Observatory for Human Rights says 20 people were killed in the blasts. The activist group relies on reports from the ground.
The SANA state news agency says the Wednesday morning explosions targeted Damascus' eastern Jaramana suburb, which is mostly populated by Christians and Druse.
Rebels fighting to topple President Bashar Assad are predominantly members of the Syria's Sunni Muslim majority. They have frequently targeted the country's minority communities, perceived to be allied with Assad's Alawite sect, an offshoot Shiite group that dominates the regime.
Damascus suburbs have become opposition strongholds since March last year, when the uprising began.
At least 40,000 people have been killed in the civil war, according to activists.
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