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The attacks left 55 others injured.
A source at Damascus countryside police command told SANA news agency of the country that the first blast occurred by a suicidal who blew up a belt at the entrance of Assayidah Zainab town while the second was by a booby-trapped car at al-Tin Street at the vicinity of the town.
Several houses and vehicles have been damaged in the area where the blasts occurred, reports said.
Meanwhile, militant group ISIS claimed responsibility for the attack.
"Islamic State group said three militants - two carrying explosives belts and one with a car bomb - carried out the attacks in Sayyida Zeinab, 10km (six miles) south of the centre," BBC reported.