Alloush told The Associated Press that Assad was not hit but that several people in his entourage were killed or wounded.
“We had promised the Syrian people a big operation for Eid and we have delivered,” he said.
Rebels have claimed attacks against Assad or members of his government in the past that turned out to be false.
Also Thursday, Syria’s state news agency said several mortar shells also hit a Damascus suburb that is home to the golden-domed Shiite shrine of Sayeda Zeinab, killing five people and wounding 12 others. The shrine is named after the Prophet Muhammad’s granddaughter and is popular with Iranian worshippers and tourists.
Meanwhile, the leader of Syria’s exiled opposition coalition attended holiday prayers in the southern province of Daraa, his second trip inside the country since he was elected head of the Western-backed Syrian National Coalition last month.
The coalition’s spokeswoman, Sarah Karkour, confirmed the rare foray into Syria by opposition leader Ahmad al-Jarba. In a video posted by the coalition, al-Jarba, dressed in a suit, is seen talking to people, surrounded by unarmed rebels wearing fatigues.
The Syrian uprising started in Daraa in March 2011 as protests against Assad’s rule. The largely peaceful revolt turned into a civil war after opposition supporters took up arms to fight a brutal government crackdown. More than 100,000 people have been killed.
Assad’s troops have recently been on the offensive in central Syria, making advances near the border with Lebanon and in the city of Homs, an opposition stronghold. They’ve also been fighting pockets of resistance around the capital and have battled rebels in Daraa near the border with Jordan.
On Wednesday, Syrian government troops ambushed a large group of rebels trudging through a desert road northeast of Damascus, killing more than 60 fighters.
Rebels, however, have made advances in the past week in the north, where they succeeded in taking over an air base after months of fighting. They also seized a string of Alawite villages in an offensive this week in the mountains of the coastal province of Latakia, an Assad stronghold.
Surk reported from Beirut.