Hezbollah and Israel last fought a major conflict in 2006.
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 recognised by the worldwide community.
What has Israel's involvement in the Syrian war been so far?
The United States meanwhile expressed its backing of Israel for its air strikes on Syrian soil.
Tensions have also spiked across the frontier between Israel and Lebanon over Israeli plans for border wall, and Lebanese plans to exploit an offshore energy block which is partly located in disputed waters.
Things began to change over the past year, however, as the Islamic State lost territory and Assad's forces and their allies regained control of the conflict.
So the latest incident needs to be seen in the context of what is now a prolonged low-level military confrontation between Israel and Iran (and its proxies).
Separately, Iran also denounced Israeli "lies" and said Syria had the right to self-defence in response to Israeli air raids.
Russian President Vladimir Putin and Israeli Prime Minister Benjamin Netanyahu discussed the situation in Syria in a telephone call on Saturday after heavy Israeli air strikes in the country, Interfax news agency cited the Kremlin as saying.
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Drake also gave an impromptu concert at the University of Miami , where he awarded a $50,000 scholarship to a lucky student. More good deeds included buying a van and ice cream for Overtown Youth Center, where it was clearly very much appreciated.
Why is what happened Saturday different from previous Israeli strikes?
Hezbollah leaders also say their Syrian battle experience will allow them to launch a ground invasion of Israel, in part through advanced hardened military tunnel infrastructure.
Iran's involvement in Syria in support of President Bashar al-Assad in a almost seven-year-old civil war - including the deployment of Iran-backed forces near the Israeli-occupied Golan Heights - has alarmed Israel, which has said it would counter any threat.
Israeli military spokesman Jonathan Conricus warned that Syria and Iran were "playing with fire", but stressed his country was not seeking an escalation. If it is true, however, it would appear to mark a significant provocation from Tehran and perhaps even an attempt to bait Israel into a reaction.
Syria responded with "substantial Syrian antiaircraft fire" under which two Israeli pilots ejected from their F-16, which crashed inside Israel, according to the Israeli military. The pilots were taken to a nearby hospital.
Katz noted that Saturday's events did not "spill over into Hezbollah", something he said was a sign of Israel's deterrent capabilities.
Hezbollah said in a statement: "Today's developments mean the old equations have categorically ended". In response to the crash, the IDF said it struck 12 Iranian and Syrian targets in Syria, including air defense batteries.
Iranian and Quds forces have been working for a while from the Syrian T4 air force base near Palmyra, Syria, supported by Syrian armed forces and with the approval of the Syrian government.
The Israel Army on Saturday shot down a Syrian drone carrying out a reconnaissance mission over the Israel-occupied Golan Heights. But the tit-for-tat fighting shows that neither side is willing to back down.