The Israeli military denied reports by Arabic media it had responded to the attacks with artillery fire, Israeli broadcaster Arutz Sheva reported.
Officials said bomb shelters in the northern city of Akko had been opened and advised residents to stay close to the shelters.
Lebanese media said at least two rockets were fired from the city of Tyre.
Three of the rockets were said to have fallen in "open areas," while the fourth was intercepted by the Iron Dome missile defense system.
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Sweden recognizes Palestinian state