Israel has bombed the al-Kiswah area for allegedly hosting Iranian missile bases, according to the report.
The report said among the areas hit was the countryside of Kisweh, home to military bases, just south of Damascus.
In Kisweh, "the depots that were targeted are used to temporarily store rockets until they are taken somewhere else", Abdel Rahman said.
Israel's military said Thursday night that Syria fired a missile at the Israeli-occupied Golan Heights after Damascus said Israel launched airstrikes on targets in southern Syria.
On September 17, a Syrian S-200 surface-to-air missile shot down a Russian Il-20 plane during an Israeli attack in Syria's Latakia, killing 15 Russian troops.
However, a surface-to-air missile was sacked at an open area in the Golan Heights and IDF forces are searching the area for additional hits.
Earlier, Syrian state media reported that a number of "hostile targets" close to the capital Damascus were downed by air defences. The reports did not say what that missile's target might have been.
After the September attack, during which Russian servicemen were killed by friendly fire, Moscow was quick to equip Damascus with the S-300 air defence missile system.
Syria has been in a state of civil war since 2011, with the government forces fighting against numerous opposition groups and terrorist organizations.
The move raised fears in Israel that its ability to rein in its arch foe Iran's military presence in its northeastern neighbour would be sharply reduced.
Israel is concerned that Iran's growing presence in Syria poses a threat to its own security and has struck dozens of Iranian and Iran-backed positions in Syria over the course of the country's seven-year conflict.