Three armed members of Hamas were killed as Israeli tanks, armoured vehicles and bulldozers entered the Palestinian town of Beit Hanun before dawn on Sunday.
Israel has repeatedly raided Gaza since the capture of one of its soldiers, Corporal Gilad Shalit, on June 28.
Gunfire and shelling also killed a 75-year-old woman and wounded 10 others, including a baby.
Israel carried out further air strikes overnight against armed Palestinians and destroyed a Hamas operations room in the Jabaliya refugee camp, an Israeli army spokeswoman said.
Israel’s campaign to free its free captured soldier has so far left 82 Palestinians and one Israeli soldier dead.
Hamas, like the Hezbollah group in Lebanon, which is holding two Israeli soldiers, demands the release of prisoners held in Israeli jails in exchange for freeing the captive serviceman.
Hamas is the ruling party in the Palestinian territories but it also advocates the destruction of Israel, which it frequently attacks with home-made rockets.