The Britain-based Syrian Observatory for Human Rights said airstrikes targeted an area near the airport while others hit the area of Kiswa, which is home to positions and storage sites for Iranian and Hezbollah terror forces allied with Syria's government.
Only recently has it begun to speak publicly about thwarting the weapons smuggling from Iran through Styria into Lebanon.
The outgoing IDF chief of staff has acknowledged that Israel has been bombing Syria on a "near-daily" basis for years, in a massive military campaign allegedly aimed at degrading Tehran's supposed military buildup in the region.
Hezbollah and Israel last fought a war in 2006.
Last month, Israel launched an operation to detect and destroy what was described as a vast network of Hezbollah tunnels, and officials say the latest discovery brings the mission to an end.
Israel and the United Nations say the tunnels violate a ceasefire resolution made after a 2006 war between Israel and Hezbollah.
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Although there are more tunnels on the Lebanese side of the border, the military says this effectively marks the end of the operation. In a New York Times interview published Friday, Eisenkot said that Israel "has struck thousands of targets without claiming responsibility or asking for credit" as part of his showdown with Qassim Suleimani, the commander of Iran's elite Quds Force.
Missile fire is seen from Damascus, Syria on May 10, 2018.
Since then Israel has been very careful with its operation over Syria.
The military said its forces will remain in the border area to monitor any further underground activity.
The powerful Shia militant Hezbollah, which acts independently in Lebanon, has yet to comment on the Israeli discoveries.
Israel said on Sunday it had completed a search for Hezbollah tunnels from Lebanon after uncovering at least six of the passages dug secretly under the border by the Iranian-backed guerrillas.