Four other members of Hamas were reported injured in the attacks, The Jerusalem Post reported.
The strikes followed a Qassam rocket attack that hit an elderly couple's home in Sderot; the couple were away at the time of the strike, news reports said. Four Qassam rockets were fired at Israeli targets Tuesday morning from the Hamas-controlled Gaza Strip.
Israel opened a crossing into the Gaza Strip, allowing trucks carrying food and medical supply to enter the area. Three truckloads were donated by the Jordanian government and another two were ordered by the Palestinian health minister from an Israeli pharmaceutical conglomerate.
Also Tuesday, official Israeli censorship was lifted on reporting a Katyusha rocket fired recently from the Gaza Strip hit near the home of Israeli Public Security Minister Avi Dichter in Ashkelon.
Late Monday, the Israeli air force fired a missile at a group of Palestinian militants allegedly firing rockets from the Gaza town of Beit Hanun, killing one man, Palestinian officials said.