An Israeli army spokesman said he would not comment on the "foreign reports".
Israel has struck Syria several times since the start of the three-year conflict, mostly destroying weaponry such as missiles that Israeli officials said were destined for their long-time foe Hezbollah in neighbouring Lebanon.
"The Israeli enemy committed aggression against Syria by targeting two safe areas in Damascus province, in all of Dimas and near the Damascus International Airport," state television said, adding that there were no casualties.
Residents in Damascus said they heard loud explosions and opposition activists posted photos online of jet streams in the evening sky and fiery explosions. Syria's army general command said on state television that there were "material losses in some facilities." It said the strike benefited al Qaeda.
Syria's state news agency SANA said the strikes were a "flagrant attack on Syria", while the official news agency in Lebanon said Israeli jets breached its airspace on Sunday.
A resident in the Damascus suburb of Qudsaya, close to Dimas, said the agricultural airport in Dimas was hit.
Dimas is in a mountainous area to the northwest of the capital which is under government control and close to several military installations.
The Syrian Observatory for Human Rights, which tracks the conflict through a network of sources on both sides, said that 10 explosions were heard near Dimas. It said that one missile hit a warehouse for imports and exports at the Damascus international airport.
Syrian state media reported in May 2013 that Israeli aircraft struck in three places including the Dimas airport. At the time, Western and Israeli officials said it was a strike on Iranian missiles bound for Hezbollah.
Syria's war started with a pro-democracy movement which grew into an armed uprising and has inflamed regional confrontations. Some 200,000 people have died, the United Nations says.
A US-led coalition is also bombing Syria from the skies but targeting the Islamic State militant group, one of President Bashar al-Assad's biggest foes.
