The Levant Liberation Committee said in a statement that the attack was carried out by two of its suicide attackers, claiming that they targeted pro-Iranian and pro-government militiamen. It identified the suicide attackers as Abu Omar and Abu Aisha.
The Syrian government maintains that the attacks killed 40 people. However the Britain-based Syrian Observatory for Human Rights increased its estimated death toll on Sunday to 74. Conflicting casualty estimates are common in the aftermath of violence in Syria.
The attacks in Damascus show that Syrian militant groups can still strike deep inside the capital where security is tight, with scores of checkpoints that search cars and ask people for identity cards.
The claim of responsibility comes at a time when al-Qaida's branch in Syria known as the Fatah al-Sham Front is trying to market itself as the only effective force against Assad and the main defender of the country's majority Sunnis.
Fatah al-Sham is opposed to peace talks between the opposition and the government that have taken place recently in Geneva and the Kazakh capital of Astana. Fatah al-Sham as well as the Islamic State group have been excluded from a cease-fire brokered by Russia and Turkey that went into effect on Dec. 30.
Saturday's attack also wounded over a hundred, most of them Iraqis, according to Syrian and Iraqi officials. The al-Qaida-linked group said the blasts were a message to Iran — a main backer of Assad. "Iran and its militias have, from the start of the revolution, supported the tyrannical and criminal regime and have been killing and displacing our people," the statement said. "This is a message to Iran and its militias that the right will not go wasted."
The Levant Liberation Committee is a coalition of several militant groups dominated by Fatah al-Sham. The attacks came two weeks after members of the same group stormed two different security offices in the central city of Homs, killing and wounding scores of people, including a top Syrian security official.
In northern Syria, opposition activists said a suspected U.S.-led coalition airstrike hit a school in the village of Kasrat just south of the city of Raqqa, killing at least 17 people. The airstrike came amid an offensive by U.S.-backed Kurdish-led fighters against the Islamic State group in the northern province of Raqqa that is home to the extremists' de facto capital.
The Observatory said Sunday's early airstrike killed 19 people, including eight who fled violence in the nearby province of Aleppo. The activist group Raqqa is Being Slaughtered Silently said the airstrike killed 17.
On Thursday, at least 20 civilians, including some children, were killed in suspected U.S.-coalition airstrikes on a village east of Raqqa. Also Sunday, two Syrian opposition figures said the Syrian armed opposition will not take part in a meeting planned and sponsored by Russia and Turkey in the Kazakh capital of Astana on Tuesday, saying the government has not been abiding by a cease-fire.
Ahmad Ramadan told The Associated Press via a text message that rebels will not go because the Syrian government and Russia are working on displacing people from the neighborhood of al-Waer, the only rebel-held area in the central city of Homs.
Rebel legal adviser and spokesman Osama Abo Zayd wrote on his Twitter account that "the crimes by the regime and Iran, and the shelling and airstrikes of Russia and its sponsoring of displacement in al-Waer has totally severed the opportunities of our participation in Astana."
The announcement came a day after Syria's armed opposition groups called for postponing the meeting in Astana, saying that violations of a Russia-backed cease-fire have persisted.