The Israeli military reported that anti-tank missiles from Lebanon targeted a military base and vehicles and responded with fire in southern Lebanon.
The Iranian-backed Hezbollah group in Lebanon said its fighters destroyed an Israeli military vehicle, killing or wounding those inside. There was no immediate word from the Israeli army about any victims.
Israel was on alert for a possible confrontation with Hezbollah last week after drones attacked what regional security officials described as a target in a Beirut suburb connected to precisely guided missile projects.
The Hezbollah leader said last Saturday that his field commanders were ready to respond to the drone attack he blamed on Israel.
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Among Hezbollah's threats, Israel had shifted reinforcements to the border area, which had been largely silent since both long-time enemies fought a month-long war in 2006.
In a statement, the Israeli army claimed that several anti-tank missiles were launched by Lebanon on Sunday and "numerous blows have been confirmed".
Following the missile attacks, the Israelis living near the border were commissioned by the authorities to stay at home. Reuters television showed smoke rising along the border and explosions could be heard.
On Sunday, the Lebanese military said an Israeli drone had dropped incendiary material and lit a fire in a pine forest on the border.
The fires near the border in Lebanon "originate from the operations of our forces in the area", said the Israeli army in a statement, without elaborating.
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Without claiming responsibility for the drone attack last week, the Israeli army published what it said were details about a vast Iran-sponsored campaign to provide Hezbollah with the means to produce precisely guided missiles .
These missiles – which Hezbollah acknowledges to possess – could potentially constitute a counterweight to Israel's overwhelming military force in any future war, with the capacity to host and destroy basic infrastructure sites.