Barak said Israel would not tolerate any attacks on soldiers or citizens "within its sovereign territory" and called on the international community to condemn the "criminal act carried out by the Lebanese army."
Prime Minister Benjamin Netanyahu also warned Lebanon, saying that it held the Lebanese government "directly accountable for this violent provocation against Israel."
The attack on IDF soldiers Tuesday is a "blatant violation of Security Council Resolution 1701," he said.
Earlier, Israel filed complaint with the UN Security Council over the exchanges of fire with Lebanese forces that left Lieutenant-Colonel (res.) Dov Harari (45) dead.
Israel files UN complaint
In the complaint it lodged, Israel said Lebanese soldiers opened fire despite the fact that the IDF had informed UNIFIL forces in advance of its plan to cut down a tree along the border fence, some 80 meters south of the border.
Speaking at a press briefing earlier Tuesday, Major General Gadi Eisenkot said Israeli troops operating near the border fence encountered a "planned ambush" by Lebanese forces.
"It was a planned ambush by a sniper unit…this was a provocation by the Lebanese army," he said. "We view this fire was a highly grave incident. Our forces responded at once, and immediately after that we resorted to artillery and gunship fire."
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Yitzhak Benhorin and Hagai Einav contributed to the report