State media said air defence forces were confronting what it said was an Israeli attack aimed at targets in the vicinity of the Syrian coastal province of Tartous.
It said the forces were also confronting “hostile targets” over the Qalamoun mountains near the border with Lebanon.
A Syrian military statement said there were two simultaneous Israeli attacks, a missile attack targeting the countryside near the capital, Damascus, carried out from the direction of southeast of the Lebanese capital, Beirut.
The other came from the direction of the sea, aimed at points south of Tartous. Air defences forces shot down some of the missiles, but there was “some material damage”, the statement added.
Syria’s state news agency Sana said fires caused by the attacks were controlled, without specifying where they had broken out.
The Israeli military declined to comment on reports of a possible strike in Syria.
Israel has been carrying out strikes for years against what it has described as Iranian- and Iran-backed targets in Syria, where Tehran has deployed forces in support of President Bashar al-Assad since the Syrian war began in 2011.
The first ship to leave Ukraine under a deal to resume grain exports from the country two weeks ago was approaching the Syrian port of Tartous on Sunday, two shipping sources told Reuters earlier.
(Reporting by Nayera Abdallah; Additional reporting by Maayan Lubell in Jerusalem; Editing by Alexander Smith and Nick Macfie.)