The confrontation was the most serious between arch foes Israel and Iran since the civil war in Syria began in 2011.
Israel’s raids came after it intercepted what it said was an Iranian drone entering its airspace from Syria, which it labelled an “attack.”
It was the first time Israel has publicly acknowledged attacking what it identified as Iranian targets in Syria since the conflict started.
Iran denounced Israeli “lies” and said Syria had the right to self-defense in response to Israeli strikes.
Separately, Iran issued a joint statement with the Syrian regime’s other main allies — Russia and Lebanese militant group Hezbollah — denying the allegations regarding the drone.
Russia’s foreign ministry called for “restraint” from all parties, adding it was “unacceptable to create threats to the lives and security of Russian soldiers” in Syria.
Israeli military spokesman Jonathan Conricus warned that Syria and Iran were “playing with fire,” but stressed his country was not seeking an escalation.
“This is the most blatant and severe Iranian violation of Israeli sovereignty in the last years,” Conricus told journalists.
Israel said its reprisals after the exchange were “large-scale” raids that attacked Syrian air defense systems and Iranian targets.
“Twelve targets, including three aerial defense batteries and four Iranian targets that are part of Iran’s military establishment in Syria were attacked,” a military statement said.
Israel has repeatedly warned in recent weeks against the presence of Iranian forces in neighboring Syria.
The two Israeli crew of the crashed F16 were alive, although one was severely wounded, the military said.
Israel’s military said the confrontation began with the drone entering its airspace before being intercepted by a combat helicopter.
Conricus said it was intercepted well inside Israel over the city of Beit Shean, near the border with Jordan.
He did not say whether the drone was armed or for reconnaissance, but alleged it “was on a military mission sent by Iranian military forces” from an “Iranian base” in the Palmyra area.
Eight Israeli aircraft then “targeted the Iranian control systems in Syria that sent the UAV” and confirmed hits, Conricus said.
He said the aircraft met “massive Syrian anti-air fire,” and the F16 later crashed in northern Israel’s Jezreel valley.
Conricus said the jet probably crashed as a result of the anti-aircraft fire, without saying definitively.
According to the military, the pilots ejected, landed in Israel and were taken to hospital.
Syria said its air defenses repelled two Israeli raids on its military bases in the center of the country, hitting more than one warplane during the first.
The Syrian Observatory for Human Rights, a Britain-based monitor of the seven-year civil war, said the earlier Israeli raids had targeted several military bases in the east of the central province of Homs.
It said the bases are used by both Iranian and Russian military personnel deployed in support of the regime.
Syrian state media said the later raids targeted military positions in the south.
Iranian foreign ministry spokesman Bahram Ghasemi said that “to cover their crimes in the region, Israeli officials are resorting to lies against other countries.”
He said “Iran does not have a military presence in Syria, and has only sent military advisers at the request of the Syrian government.”
Iran, Russia and Hezbollah — the Syrian regime’s main allies — issued a statement calling Israel’s drone allegations “lies.”
It said Israel’s strikes had targeted drones used against “terrorist organizations,” mainly the Daesh group.
The statement vowed a “relentless response” to “all further aggression.”
Israeli Prime Minister Benjamin Netanyahu met officials including Defense Minister Avigdor Lieberman and military Chief of Staff Gadi Eisenkot later Saturday.
He has held a series of talks in recent months with Russian President Vladimir Putin on Iran’s influence in Syria and Lebanon.
Netanyahu has been seeking to persuade Russia to limit Iran’s presence near Israel and to stop it from entrenching itself militarily in Syria.
In Moscow last month, Netanyahu reiterated concerns over what he called attempts by Iran to establish a military presence in Syria and produce weapons against Israel there.
“We won’t accept either of those, and will act according to our needs,” he said.
Israel remains technically at war with Syria and occupies a swathe of the strategic Golan Heights that it seized in the Six-Day War of 1967 and later annexed in a move never recognized by the international community.
On Tuesday, Netanyahu took members of his security cabinet for a tour of the Israeli-occupied side, where they were briefed by the military.
Israel has sought to avoid direct involvement in the Syrian war, but acknowledges carrying out dozens of air strikes there to stop what it calls advanced arms deliveries to Hezbollah.
Analysts said they did not expect a further escalation for now, but suggested the heavy anti-aircraft fire showed Syria was more emboldened to stop Israel’s strikes.
Ofer Zalzberg of the International Crisis Group said Russia should mediate since “it is the only stakeholder which has strong relations with all sides today.”
But he said “this incident signals a new phase in a way of the war in Syria.”