"At around 23:05 (2105 GMT) the Israeli enemy carried out an air assault... targeting various points on the outskirts of Damascus," a security source told the agency.
"Our anti-aircraft defences shot down some missiles while others caused limited material damage."
An AFP correspondent reported strong explosions in the suburbs of Damascus, which have been previously targeted by strikes that Syrian authorities have blamed on Israel.
The Syrian Observatory for Human Rights, a Britain-based war monitor, said the strikes had targeted "Hezbollah sites" in the Sayeda Zeinab district and near Damascus airport.
The Israeli army declined to comment on the incident, but said separately that shots had been fired from Lebanon towards northern Israel on Sunday evening.
"The army retaliated by targeting the source of the fire. Earlier in the day, we had struck a Hezbollah terrorist cell," it said in a statement.
Israel's army chief Herzi Halevi visited his forces near the northern border with Lebanon on Sunday, where he spoke of the need "to kill Hezbollah operatives, to demonstrate our superiority".
"It can also come in the form of a strike and war," he said.
Israel rarely comments on individual strikes targeting Syria, but it has repeatedly said it will not allow arch-foe Iran, which backs Syrian President Bashar al-Assad, to expand its presence there.
Israel has launched hundreds of air strikes on its northern neighbour since Syria's civil war began in 2011, primarily targeting Iran-backed forces including Hezbollah fighters, as well as Syrian army positions.
But it has intensified attacks since its war with Hamas began in October. Hamas last year said it had restored relations with Syria's government.
Three Hezbollah fighters and a Syrian were killed on Friday in an Israeli drone strike on their car in the south of Syria, the war monitor said.
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