In a statement carried by state media, the army claimed Israel attacked Syrian territory with jets and ground-to-ground missiles early on Tuesday, causing damage.
The statement says several missiles were first launched from inside Lebanese airspace at 2:40 a.m., followed by two more missiles at 3:04 a.m. and four at 4:14 a.m.
The letter also reads that the Israeli attacks are mostly aimed at increasing the "shallow morale" of the terrorist organizations operating in the area targeted by the alleged airstrike.
The Israeli military declined to comment on the matter.
There are reports of surface-to-surface missiles being fired and of local residents hearing explosions.More news: New England Patriots: Bill Belichick quickly slams door on reports
This article has been adapted from its original source.
Prime minister Benjamin Netanyahu, speaking to ambassadors of North Atlantic Treaty Organisation countries in Israel, said: "We have a long-standing policy to prevent the transfer of game-changing weapons to Hezbollah from Syrian territory".
In its statement, the Syrian army repeated previous warnings of serious repercussions for the strikes and repeated its past accusation that Israel was using attacks to support militant groups in Syria.
Israeli Prime Minister Benjamin Netanyahu said in answer to a reporter's question about the strikes that Israel's policy was to stop Hezbollah moving "game-changing weapons" out of Syria.
The exact target of the strikes could not be independently confirmed.