No damage or injuries were reported in the incidents.
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The Israeli Air Force struck cannons belonging to the Syrian regime late Tuesday evening in response to a number of mortar rounds that fell into Golan Heights just hours earlier, according to a military statement.
In a statement, the army said Israeli warplanes had targeted artillery batteries deployed by the Assad regime in the Syrian Golan Heights after three projectiles were fired into northern Israel from Syrian territory earlier Tuesday.
The Israeli army said none of its aircraft had been downed overnight on Monday, as claimed by Syria, and it carried out fresh strikes against Syrian artillery positions on Tuesday night.
Syrian state media has said the army has shot down an Israeli warplane and a drone after an Israeli attack on Syrian military position in Quneitra, near the Israeli border.
On Monday evening, Syrian fire crossed into the northern Golan Heights as a nationwide ceasefire brokered by the United States and Russian Federation came into effect in the embattled country.
The Israeli military denies the shootdown but confirms recent airstrikes on Syria.
There were similar events in July and previously.
Several stray rockets and shells have landed in Israel since the start of the civil war in Syria more than five years ago.
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Israel seized 1,200 square kilometres (460 square miles) of the Golan Heights from Syria in the Six-Day War of 1967 and later annexed it in a move never recognised by the worldwide community.
