The Israeli Defense Forces (IDF) claimed that mounting violence began on Wednesday after militants shot at an IDF vehicle in Gaza.
The IDF confirmed they responded by firing at 140 targets in Gaza. Eight Palestinian civilians were also wounded.
Hamas has been the de facto ruling party in Gaza since winning contested Palestinian parliamentary elections in 2006. One Israeli soldier was shot dead by a Palestinian sniper.
The military said it intercepted some 25 rockets, while most of the others landed in open areas.
Israeli Ynet News said that one Israeli man, aged 23, was injured by shrapnel in his leg, and added that "two pregnant women in addition to a man, 42 years of age, were treated for shock", before being moved to Barzilai Hospital.
Sirens sounded in Israeli areas near Gaza, warning residents to seek immediate shelter, the Israeli army said.
Gaza's Health Ministry said three Palestinians were slightly injured in the strikes.
Jamie McGoldrick, the United Nations' humanitarian coordinator for the Palestinian territories, in a news release called Israel's restriction of fuel imports "a risky practice, with grave consequences on the rights of people in Gaza".
A senior military source said that he believes the attacks will continue and that if necessary Israeli villages and towns will be evacuated.
The violence came after two fighters from the military wing of Hamas, which governs Gaza, were killed by Israeli fire on Tuesday.
Lt. -Col. Jonathan Conricus, an Israeli army spokesperson, insisted Israel only targeted Hamas military targets in Gaza. The rockets, of course, are pretty inaccurate, and just getting them into southern Israel seems to be the best Hamas can manage.
Incoming rocket sirens continued to wail throughout southern Israel, including the city of Ashkelon, as projectiles continued to be launched from the Gaza Strip on Thursday as Israeli jets and tanks continued to pound the coastal enclave.
Israeli Prime Minister Benjamin Netanyahu called off a trip to Colombia this week to attend to the Gaza truce talks and was due to convene his decision-making security cabinet on Thursday to discuss the situation.
Both sides have said they are working toward a cease-fire agreement, though continued rocket fire may dampen efforts.
Smoke plumes could be seen rising from Gaza City after Israel launched the strikes.
"The Israeli strike was conducted in response to the rockets launched from the Gaza Strip at Israeli territory over the course of the evening and night", it said in a statement.