Israel has activated a plan to evacuate residents of 28 villages within 2 km (1 mile) of the Lebanese border, the military said on Monday following hostilities with Hezbollah in parallel to the spiraling war in Gaza.
One of the villages, Shtula, came under a Hezbollah missile attack on Sunday. Israeli media said a civilian was killed.
Lebanese Hezbollah fighters launched attacks on Israeli army posts and a northern border village on Sunday, and Israel retaliated with strikes in Lebanon as UN peacekeepers warned border clashes were escalating.
Sporadic fire across the Israel-Lebanon border over the past week has raised concerns that fighting with Hamas militants in Gaza could escalate into a broader conflict.
Hezbollah's attack on Shtula, a farming community that abuts the border fence, killed one person and wounded three others, the militant group and Israeli medics said, as the worst border-violence since a month-long war in 2006 entered its second week.
Hezbollah also said it had targeted barracks in Israel's Hanita with guided missiles and said it had inflicted casualties on "the enemy ranks".
The Israeli military said it had conducted strikes in Lebanon in retaliation and it declared a zone within 4 km (2 miles) of the Lebanese border off-limits to public access.
Three security sources confirmed to Reuters that Israeli artillery had struck several areas in the south.
Hamas' armed wing, Al Qassam Brigades, said it had fired 20 rockets from Lebanon on two Israeli settlements.
United Nations peacekeeping force UNIFIL said its headquarters in south Lebanon had been hit by a rocket but no one was injured. It said it was working to determine where the projectile had come from.
"We continue to actively engage with authorities on both sides... but regrettably despite our efforts military escalation continues," it said in a statement.
Israel's defense minister said on Sunday that Israel has no interest in waging war on its northern front and that if Hezbollah restrains itself then Israel will keep the situation along the border as it is.
"We have no interest in a war in the north. We don't want to escalate the situation," Defense Minister Yoav Gallant told reporters.
"If Hezbollah chooses the path of war, it will pay a very heavy price. Very heavy. But if it restrains itself, we will respect that and keep the situation as it is," Gallant said.
Hezbollah has said it is ready to fight Israel and that it would not be swayed