The Syrian Observatory for Human Rights said the strikes in Damascus's Kafr Sousa district targeted "the courtyard of a government building near a military fuel station".
"One person whose identity is unknown" was killed and three others wounded, the Britain-based war monitor said.
In Homs province, which borders Lebanon where Israeli troops are fighting Hezbollah, the Israeli strikes "targeted a truck near a regime forces checkpoint on the road on the outskirts of Qusayr".
That attack killed a soldier and wounded four others, the Observatory said.
Syrian state news agency SANA said the Israeli army "launched an air attack... targeting two sites" in the Kafr Sousa district of Damascus and a military site near Homs. It reported one soldier killed and seven others wounded.
Since the civil war erupted in 2011, Israel has carried out hundreds of strikes in Syria, mainly targeting the army and Iran-backed armed groups, including Hezbollah.
The Israeli military has intensified its strikes since it launched its war on Hezbollah in neighbouring Lebanon last month.
Israel rarely comments on individual strikes in Syria, but has repeatedly said it will not allow Iran to expand its presence.
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