Early assessments suggested that the Israeli F-16 had been hit by Syrian anti-aircraft fire, according to a military spokesman, Lt Col Jonathan Conricus.
In response to the drone infiltration, the IDF attacked the Iranian T-4 center with eight fighter jets, which came under significant Syrian anti-aircraft fire, Conricus said.
"We can hear the sounds of the explosions", said one Damascus resident, who spoke on the condition of anonymity.
The Syrian attack resulted in air raid sirens being activated in the Golan Heights and Beit She'an, but no casualties were reported.
"Our air defenses confronted it and hit more than one plane", the unidentified military source said.
Meanwhile, Lebanon's National News Agency reports an errant anti-aircraft missile "fired by the Israeli enemy" fell in a Lebanese citrus grove.
One of those planes, a USA -made F-16, crashed on its return from that mission, landing in an empty field near Harduf, east of Haifa, in northern Israel.
"We won't accept either of those, and will act according to our needs", Netanyahu said then. All regional players must "exercise restraint and avoid any action that could further complicate the situation", the foreign ministry said in a statement, stressing the need to respect the sovereignty of "Syria and other nations in the region".
Israel's raids came after it intercepted what it said was an Iranian drone entering its airspace from Syria, which it labelled an "attack".
"We identified an Iranian drone UAV which took off from Syrian territory".
Israel has been warning lately of increased Iranian involvement along its border in Syria and Lebanon.
The drone, which Israel said was launched from Syria, was shot down by an Israeli helicopter after what the military called a "severe and irregular violation of Israeli sovereignty".
"It is absolutely unacceptable to create threats to the lives and security of Russian servicemen who are in Syria at the invitation of its legitimate government to assist in the fight against terrorists", the ministry said. The F-16 fighter was on a mission to strike Iranian drone installations in Syria, where Iranian and Iran-backed forces have established a major foothold while fighting in support of President Bashar al-Assad.
Israel has mostly stayed out of the prolonged fighting in Syria, wary of being drawn into a war in which almost all the parties are hostile toward it.
Just last month, Israeli Prime Minister Benjamin Netanyahu visited Moscow for talks about Syria, specifically the growing influence of Iran.
Hezbollah in a separate statement said the F16's downing marked the start of a "new strategic era".
Analysts in Israel say it was a chemical weapons factory.
In an attempt to contain Iran and its proxies, Israel has regularly carried out airstrikes inside Syria, though it has in the past refrained from acknowledging its responsibility for specific bombings.
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