The Levant Liberation Committee, operating under the rebel alliance Hayat Tahrir al Sham, said the blasts were a message to Iran, a key supporter of the Syrian regime.
A faction operating under the Syrian alliance of rebel groups known as Hayat Tahrir al Sham said on Sunday it was responsible for a double suicide bomb attack on Saturday in the capital Damascus that killed at least 74 people.
The Levant Liberation Committee said the attack was carried by two of its suicide attackers who targeted pro-Iranian and pro-government militiamen.
The faction said the blasts were a message to Iran, a main supporter of the Syrian regime.
The group said the attack was revenge for Iran's role in supporting Bashar al Assad's "tyrannical rule," holding the regime responsible for "killing and displacing" Syrians.
The Syrian Observatory for Human Rights (SOHR), a British-based war monitor, said most of those killed in the attack were Iraqi Shia pilgrims who were going to visit a cemetery near the Old City of Damascus.
It said at least 20 regime soldiers also died.
Iranian-backed Shia militias from countries that include Iraq, Afghanistan and Lebanon are backing Assad in his six-year war against mainly Sunni Muslim rebels.
Many rebel groups say Iranian-backed militias are trying to evict Sunnis from around Damascus and other areas that are strategically important in the war.
Hayat Tahrir al Sham was created from a merger of Jabhat Fateh al Sham – formerly al Qaeda's Nusra Front – and several other groups.
The rebel alliance is not linked to Daesh.