The military's Home Front Command said schools and other educational institutions and activities would not be permitted in the north until at least Monday at 6:00 pm (1500 GMT).
Gaza war intensified: Hezbollah hits northern Israel by launching 100 rockets within 60 minutes
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The Israeli military said more than 100 projectiles were fired from Lebanon early Sunday, with fire services working to put out blazes sparked by falling munitions in Israel's north.
Lebanese group Hezbollah has exchanged regular fire with Israeli forces throughout the Gaza war, but the cross-border violence has intensified in recent days.
The military said that "approximately 20 projectiles were identified crossing from Lebanon" shortly before 5:00 am (0200 GMT), followed by a barrage of "approximately 85 projectiles" launched from Lebanon after 6:00 am (0300 GMT).
Rockets were also fired during the night, the military said. Israel's medical emergency service, Magen David Adom, said in a statement that four people were wounded from shrapnels during the night.
The military also reported attacks from the east.
During the night, "multiple suspicious aerial targets" approached Israel from the direction of Iraq, the military said, adding they were intercepted and caused no injuries.
Israel army says striking Hezbollah targets in Lebanon after rocket fire
The Israeli military said it launched new strikes on Hezbollah targets in Lebanon early Sunday after the Iran-backed group fired dozens of rockets towards northern Israel.
"The IDF (military) is currently striking targets belonging to the Hezbollah terrorist organisation in Lebanon," a military statement said, adding that the group had fired some 115 projectiles "towards civilian areas in northern Israel" over the past few hours.
Israel defence agency orders schools shut in northern areas near Lebanon
Israel's civil defence agency on Sunday ordered all schools in the country's north closed following rocket fire by Lebanese armed group Hezbollah and intensifying cross-border violence.