Israel's military said on Sunday anti-tank missiles from Lebanon targeted an army base and vehicles and that it responded with fire into southern Lebanon.
Lebanon's Iran-backed Hezbollah group said its fighters destroyed an Israeli military vehicle, killing or wounding those inside.
There was no immediate word from the Israeli military on any casualties.
Israel has been on alert for a possible confrontation with Hezbollah for the past week after drones attacked what security officials in the region described as a target in a Beirut suburb linked to precision-guided missile projects.
Hezbollah's leader said late on Saturday that the group's field commanders were ready to respond to the drone attack, which he blamed on Israel.
Meanwhile, Lebanese Prime Minister Saad Al Hariri called the US Secretary of State and France's top diplomat on Sunday "asking the United States and France to intervene in the face of developments at the southern border."
The head of the UN peacekeeping force in Lebanon urged "maximum restraint".
"UNIFIL is following up on the firing across the Blue Line" between Lebanon and Israel, said Andrea Tenenti, spokesman for the UN Interim Force in Lebanon.
Amid the Hezbollah threats, Israel had moved reinforcements into the border area, which had been largely quiet since both longtime enemies fought a month-long war in 2006.
In a statement, the Israeli military said several anti-tank missiles were fired from Lebanon on Sunday and "a number of hits were confirmed".
Following the missile attacks, Israelis living near the frontier were instructed by authorities to stay indoors.
Reports showed smoke rising along the frontier and the sound of explosions.
Earlier on Sunday, the Lebanese military said an Israeli drone had dropped incendiary material and sparked a fire in a pine forest by the border.
The fires near the border in Lebanon "originate with operations by our forces in the area," the Israeli military said in a statement, without elaborating.
Without claiming responsibility for the drone attack last week, the Israeli military published what it said were details about an extensive Iranian-sponsored campaign to provide Hezbollah with the means to produce precision-guided missiles.
Such missiles – which Hezbollah acknowledges possessing – could potentially pose a counter-balance to Israel’s overwhelming military force in any future war, with the capacity to hone in on and knock out core infrastructure sites.
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