According to the IDF, the rockets were launched from the Hamas-run enclave and two were intercepted by the Iron Dome missile defence system.
There are also reports that the Israeli Air Force (IAF) has carried out drone strike on multiple locations in Gaza, but this is unconfirmed.
In a written statement, the Ezzeddin Qassam Brigades, the military wing of Hamas, claimed responsibility for the attacks.
Gaza's Health Ministry said three Palestinians were slightly injured in the strikes.
Air raid sirens sounded nearly nonstop in southern Israel from sundown on Wednesday, warning residents to stay in shelters as more than 80 rockets were fired in their direction.
Two homes in Sderot were also reportedly hit by the shrapnel and several cars were damaged.
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After approximately 70 rockets were fired from Gaza on southern Israel, IDF hit Hamas positions including a factory that produces concrete for terror tunnels.
The area where the rockets fell have been closed off by the police as bomb disposal units were called to the scene.
The two men killed in northern Beit Lahiya were Hamas snipers taking part in a live-fire exercise within a compound on Gazan territory, the group's armed wing said in a statement.
Jamie McGoldrick, the United Nations' humanitarian coordinator for the Palestinian territories, in a news release called Israel's restriction of fuel imports "a unsafe practice, with grave consequences on the rights of people in Gaza".
The Israel Defense Forces Twitter account said its fighter jets had targeted more 140 strategic sites, including a weapons manufacturing and storage facility.
Hamas warned Israel - with which it has fought three wars since 2008 - it would pay for the attack.
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More than 160 Palestinians have been killed by Israeli forces - most during weekly protests at which thousands of Palestinians have expressed their support for the declared right of Palestinian refugees to return to their ancestral homes in what is now Israel.
The escalation comes after the Hamas leadership convened for a rare meeting in Gaza on Friday.
On Tuesday, the IDF admitted that earlier shootings from Hamas did not target Israeli soldiers which caused IDF to strike back, killing two Hamas militants, Israel's Channel 10 reported.
The source, speaking on condition of anonymity, said that as part of the deal, which was brokered by Egypt and the United Nations with input from Turkey and Qatar, Hamas and Israel would initially observe a two-week trial cease-fire.
In a statement, the IDF said: "Terrorists shot at civilian vehicles that were being used in the effort to construct the barrier around the security fence in the northern Gaza Strip".
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