This comes as Israel and the United States have stepped up strikes on Iranian and Iran-aligned targets.
The strikes come just days after alleged Israeli airstrikes targeted sites in Homs in central Syria.
Syrian state media said only material damage was caused by the airstrikes.
Syrian state media said a likely Israeli attack had targeted a building in the Mazzeh neighborhood of Damascus, without giving further details.
Syrian media also claimed on Thursday evening that Israel had targeted sites in southern Syria and near Damascus with airstrikes in two separate waves.
Syrian air defenses were activated in the Damascus area during the strikes.
Three security sources and Iranian state media said an Israeli air strike outside Damascus on Monday killed Sayyed Razi Mousavi.
Iranian state-owned media confirmed the death of IRGC commander Seyed Razi Mousavi, identified as "a senior advisor" in Syria.
Ambulances reportedly rushed to the area shortly after the strikes.
Alleged Israeli airstrikes reportedly targeted several sites used by Iranian militias, including weapons storage and air defense sites.