The Palestinian group Islamic Jihad, which also has a presence in southern Lebanon, separately said one of its fighters was killed.
It is the worst escalation in violence along the Israeli-Lebanese border since a 2006 war between Hezbollah and Israel.
Sources have previously said Hezbollah's attacks were designed to keep Israel's military occupied without provoking a major war.
Israel has said it has no interest in waging war and said if Hezbollah is restrained it will maintain the status quo.
Israel and Hezbollah both reported exchanges of fire on other points along the frontier on Saturday, including around Lebanon's Alma Al-Shaab and Israel's Hanita, an area where Hezbollah said it fired guided missiles and Israel responded.
Persons:
Lisi Niesner, Israel, Alma Al, Israel's, Edmund Blair, Ros Russell, Daniel Wallis
Organizations:
REUTERS, Rights, Islamic, Hamas, Kiryat, Thomson
Locations:
Lebanon, Israel, Rights BEIRUT, JERUSALEM, Lebanese, Iran, Margaliot, Gaza, Kiryat Shmona, Israeli, Kiryat Shmona's, Jerusalem, Beirut