The attack took place at 11:15pm (21:15 GMT), it said.
The Syrian army said its air defenses intercepted most of the missiles, adding that only a warehouse in the Damascus worldwide airport was damaged.
"At 11:15, Israeli fighter jets fired several missiles towards the area of Damascus, and instantly, our air defences confronted the missiles and downed majority", the source told SANA.
"Two areas hosting military positions of Iranian forces and the Lebanese Hezbollah movement have been targeted", the Syrian Observatory for Human Rights monitor said.
A Transport Ministry spokesperson told SANA that air traffic from the airport was unaffected by the conflict.
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The 40-year-old is also trying to win for the second time this season after capturing the Mayakoba Golf Classic in November. Kuchar followed with 12-foot birdie putts on the next two holes, and he was on his way to his ninth career victory.
Israeli drones and warplanes were heard flying Friday afternoon over Lebanon.
The strikes were first reported a little before midnight in Damascus by the Syrian News Agency.
On Christmas Day, a Syrian anti-aircraft missile flew into Israeli airspace and it was destroyed by Israeli air defenses.
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He said the country is considering recommending caution towards the company, including potential exclusion from its IT market. The United States wants Meng extradited to face charges that she misled banks about the company's business dealings in Iran.
Russian Federation is a main ally of Damascus.
Syrian state media broadcast footage of the air defenses firing, with bright lights seen shooting across the night sky.
Prime Minister Benjamin Netanyahu said Sunday that Israel had at the weekend carried out an air strike on Iranian weapons in Syria, a rare public confirmation of such attacks.
Israel had previously said it will not tolerate Iran seeking to establish permanent military bases in Syria as the war there winds down after seven years of fighting.
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The Wales global is Arsenal's longest-serving playing, having moved to the Emirates from Cardiff City as a teenager back in 2008. He has also scored the winning goal in two of his three FA Cup triumphs.