Israeli planes bombed the area near Damascus international airport and the town of Dimas, media reports said. Residents said they heard explosions.
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.
Syrian state TV said the “Israeli enemy” had carried out “trespassing aggression” with the two air strikes.
However, an Israeli army spokesman told Reuters he would “not relate to the foreign reports”.
The Israeli air force has conducted several attacks on Syria since the Syrian uprising began in March 2011.
Many previous air strikes are thought to have targeted weapons being transported to the militant group Hezbollah in Lebanon.
The Israeli military has also attacked Syrian military sites in retaliation for attacks on the occupied Golan Heights.
State owned Al Ikhbariya news channel reported no casualties in Sunday’s air strikes which hit the al-Dimas suburb and near the Damascus international airport.