The three Lebanese soldiers, including one officer, were dismantling a missile near the village of Tibnine when they were killed, security officials said on Wednesday. It is unclear if the missile was from Israel or Hezbollah.
The Israeli soldier died and three others were wounded by a landmine their army had planted to stop Hezbollah fighters. Lebanese security officials said the soldiers' tank drove over the mine, but Israel said it could not confirm that.
Another Israeli soldier was shot in the head during a military operation in the border village of Taibeh, Al-Arabiya television reported. Israel would not immediately comment on that report.
Israeli soldiers entered Rub Thalatheen and kidnapped two residents, Lebanese security officials said. Lebanon's national news agency said they were brothers, Hassan and Mohammed Abed al-Hussein. It was unclear if they had any links to Hezbollah.
Shebaa Farms shelling
Meanwhile, exchanges of fire were reported near the disputed Shebaa Farms area - where the borders of Lebanon, Syria and Israel meet - but officials gave differing accounts of the clash.
The Israeli military said it fired artillery into its own territory as a means of deterrence.
Lebanese security officials, speaking on condition of anonymity, said Israeli troops fired across the border into the Lebanese village of Shebaa. The shelling lasted for three hours and hit near Lebanese army positions, they said.
Lebanese troops entered Shebaa last week for the first time in nearly four decades as part of a deployment under the UN-brokered ceasefire.
The ceasefire allows Israel to launch "defensive" military action in southern Lebanon. Hundreds of Israeli troops remain in positions they occupied during the conflict as they wait for a UN peacekeeping force to arrive.