Palestinian health officials said on Wednesday that two of the victims were a pregnant woman and her 18-month old child as the Israeli army claimed it bombed Hamas military targets in the enclave in response to rocket fires..
A Hamas militant was killed in one strike, with at least 12 others injured, the health ministry in Gaza said.
Sirens wailed in southern Israel, warning of incoming rockets from Gaza, and Israeli media reported six people were wounded by shrapnel in the border town of Sderot.
Smoke plumes could be seen rising from Gaza City following the military's announcement it was targeting "terror sites in the Gaza Strip".
Rockets fired from Gaza into Israel as seen from Sderot.
The nearly daily airborne arson attacks have been part of months of weekly border protests led by the Islamic militant group Hamas that rules Gaza aimed in part at drawing attention to the Israeli-Egyptian blockade imposed after it took control of the territory in 2007. At the same time Israeli aircraft struck 140 targets belonging to the Hamas Islamist group that controls the Gaza Strip.
According to the Israel Defense Forces, 36 projectiles were fired at southern Israel on Wednesday night, including the eight that were launched at Sderot.
Hamas's military wing said it was behind the rocket attacks.
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The Israeli army said Wednesday's violence began with militants firing guns at an Israeli engineering vehicle, and Israeli troops responding with tank fire.
A 34-year old man was lightly injured by broken glass, and damages to several cars were reported.
Israeli Prime Minister Benjamin Netanyahu convened an emergency meeting of the security cabinet due to the growing tensions in the Gaza Strip which was attended by Defense Minister Avigdor Liberman and senior commanders.
Deputy Hamas chief in Gaza, Khalil Al-Hayya, told Al Jazeera television: "We can say that actions led by the United Nations and Egypt are in advanced stages and we hope it could yield some good from them".
Wednesday's exchange came just a day after two members of the Gaza Strip's ruling Hamas movement were killed by Israeli fire. One Israeli soldier was killed by a Gaza sniper during this period.
The protests call for Palestinians to be able to return to the land they or their families fled or were expelled from in the 1948 war that established the state of Israel.
Over the past four months, 158 Palestinians have been killed by Israeli fire, including at least 120 in the protests near the fence and others in Israeli air strikes and other incidents elsewhere in Gaza, according to the Gaza Health Ministry and a local rights group.