In the first attack, Israeli jets launched several missiles that crossed Lebanese airspace towards their target in Al Qutayfah, in the province of Damascus, the statement said.
There was no comment from Israel on the claim.
According to the Syrian army, its air defense systems intercepted several missiles and struck one Israeli aircraft. Israel has conducted periodic attacks in Syria since the conflict there began in 2011, but generally does not publicly acknowledge its operations.
The Syrian statement said Israel's attack was aimed at supporting terrorist forces, to bolster them after advances of the Syrian army.
"We back it up as necessary with action", he said, without explicitly confirming Israel carried out Tuesday's strikes.
The military statement said the new aggression reflects Israel's support to the terror groups in Syria and its desperate attempt to lift their morals after the "painful blows dealt to the terror groups" by the Syrian army across the country, mainly in the city of Harasta in eastern Damascus, and the northwestern province of Idlib.
The letter claims that the "repeated and recurring" attacks on Syria prove the "Israeli Occupation Army's" hostile and risky route with its constant attempts to undermine the region's stability and entangle Syrian President Bashar al-Assad's regime.
The Observatory, which monitors the war in Syria through a network of activists on the ground, said there was no immediate word on casualties.