A military statement said that "two projectiles were identified crossing from Syria into Israeli territory, and fell in open areas", adding in a subsequent statement that its "artillery struck in southern Syria" following the launches.
Syria's official news agency SANA reported shelling "targeting the Yarmuk Basin, in the west of Daraa" province.
Britain-based war monitor the Syrian Observatory for Human Rights said bombardments had hit farmland in the province, without reporting casualties.
There were no reports of casualties or damage on the Israeli side due to the projectiles, which the military said triggered air raid sirens in parts of the southern Golan Heights, a territory Israel conquered from Syria in 1967 and annexed in 1981.
Katz, the Israeli defence minister, said in a statement released by his office that "we view the president of Syria as directly responsible for any threat or fire directed at the State of Israel."
"A full response will follow shortly," he added.
Syria's interim president, Ahmed al-Sharaa, led the Islamist group that spearheaded the offensive that toppled longtime ruler Bashar al-Assad in December.
Israeli media said Tuesday's projectiles were the first fired from Syria into Israeli territory since Assad's fall.
Following his overthrow, Israel moved its forces into the UN-patrolled demilitarised zone in the Golan Heights, and has carried out hundreds of strikes against military targets in Syria.
Israel says the strikes aim to stop advanced weapons reaching Syria's new authorities, whom it considers jihadists.
In a statement on Sunday, Israel's military said its troops were continuing "defensive operations in southern Syria" to "dismantle terrorist infrastructure and protect the residents of the Golan Heights".
Syria and Israel have technically been at war since 1948.
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