Israeli planes bombed the area near Damascus international airport and the town of Dimas, the Syrian army said in a statement carried on state television.
No casualties were reported. There has been no confirmation of the air strikes from Israel.
Israel has conducted several air strikes on Syria since 2011.
“This afternoon, the Israeli enemy targeted two safe areas in Damascus province, namely the Dimas area and the Damascus International Airport,” the military statement said.
It described the air strikes as “direct aggression” carried out to help the Syrian government’s opponents.
Some installations had been damaged, it added, without elaborating on what had been hit.
Responding to the Syrian accusation, Israel’s military said it did not comment on “foreign reports”.
The Israeli air force has conducted several air strikes on Syria since the Syrian uprising began in March 2011.
Israel generally does not comment when it carries out attacks outside its borders.
However, Israeli jets were seen constantly flying over parts of Lebanon on December 7, about 20 miles from where the alleged attacks are said to have taken place.
The Israeli military has also bombed Syrian military sites in the past in retaliation for attacks on the occupied Golan Heights.
Israel seized Golan Heights from Syria in the closing stages of the 1967 Middle East War, and thwarted a Syrian attempt to retake it in 1973.
It unilaterally annexed the area in 1981, in a move not recognized internationally.
Israel and Syria remain technically in a state of war, and UN observers are deployed to monitor a 44-mile demilitarized zone.
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