Israeli shelling on Lebanon killed at least three Hezbollah militants on Monday, and Israel said one of its officers was killed during an earlier cross-border raid claimed by Palestinians in Lebanon.
The cross-border violence marked a significant expansion of a conflict between Israel and Palestinian militants in Gaza to the Israeli-Lebanese border further north.
Iran-backed Hezbollah and Israel fought a brutal month-long war in 2006.
Hezbollah said in consecutive statements that three of its members had been killed in Israel's "aggression" on southern Lebanon on Monday afternoon. Two Lebanese security sources told Reuters two more Hezbollah members were killed.
Israel shelled southern Lebanon after a cross-border raid claimed by the Palestinian Islamic Jihad group. The Israeli Army said soldiers backed by helicopters killed at least two gunmen who crossed the frontier.
The army later said that a deputy commander, Lieutenant Colonel Alim Abdullah, was killed during the encounter. It did not provide details.
Hezbollah and Israel have traded sporadic fire over the border since 2006 while avoiding a major conflict. They exchanged artillery and rocket fire on Sunday.
Some residents of southern Lebanon said they were leaving homes along the border with Israel on Monday amid heavy shelling that had so far pounded the outskirts of towns and villages.
The state news agency reported heavy traffic on main roads due to people fleeing the border area and schools in the area will remain closed on Tuesday.
A series of incidents over the past months had already elevated the risk of escalation along the Lebanon-Israel border before the fighting erupted in Israel and Gaza.
Gabi Hage, a father of three with a house in Lebanon near the border, described heavy shelling close to him.
"Our house is really close to the border, so we're leaving and going down to the village. All my neighbors are doing the same," he said.
The French consulate in Lebanon told its nationals to postpone any travel to southern Lebanon. Britain also said tensions were high and that the situation could escalate.
(Reporting by Laila Bassam, Timour Azhari, and Maya Gebeily in Beirut and Dan Williams in Jerusalem; additional reporting by Rami Ayyub in Washington; writing by Timour Azhari; editing by Howard Goller)