Israeli planes struck the town of Kisweh approximately 20 kilometres south of Damascus, a Syrian security source and Syria TV said. The security source said a military site was targeted, without providing further details.
Additional Israeli air raids hit a town in the southern province of Daraa late on Tuesday, a resident and Syria TV said.
The Israeli military said in a statement later that it attacked military targets in southern Syria including headquarters and sites which it said contained weapons.
"The Air Force is attacking strongly in southern Syria as part of the new policy we have defined of pacifying southern Syria - and the message is clear: we will not allow southern Syria to become southern Lebanon," Israeli Defence Minister Israel Katz's spokesperson said in a statement.
"Any attempt by the Syrian regime forces and the country's terrorist organisations to establish themselves in the security zone in southern Syria - will be met with fire."
Residents of Damascus and Reuters reporters in the city heard the sound of airplanes flying several low passes over the capital and a series of blasts.
The bombardment came hours after Syria condemned Israel's incursion into the country's south and demanded it withdraw, according to the closing statement of a national summit.
Israel moved forces into a UN-monitored demilitarised zone within Syria after rebels led by Hayat Tahrir al-Sham (HTS), a former al-Qaeda affiliate, toppled former president Bashar al-Assad in December.
Israeli Prime Minister Benjamin Netanyahu said on Sunday that Israel will not tolerate the presence of HTS in southern Syria, nor any other forces affiliated with the country's new rulers, and demanded the territory be demilitarised.
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