Meanwhile, an official from the Islamist Gaza Strip government told Turkey's state-run Anadolu Agency on Wednesday that Hamas may be ready to reach an agreement toward a truce with Israel. The Iron Dome aerial defense system intercepted 11 launches, the majority of the rockets hit open areas.
"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. At least five other civilians were also wounded.
The strikes came after two fighters from the military wing of Hamas, which rules Gaza, were killed by Israeli fire on Tuesday.
The Israeli army earlier on Wednesday said Palestinians fired at least 36 rockets across the border.
Residents of Israeli communities near the Gaza border were instructed on Wednesday night to remain near protected spaces.
"Hamas hit the "enemy" with a large number of rockets", it said.
Palestinian sources said it was a drone attack, while the Israeli statement said it was tank fire.
A 34-year old man was lightly injured by broken glass, and damages to several cars were reported.More news: Mourinho hopes World Cup players can feature in opener
After approximately 70 rockets were fired from Gaza on southern Israel, IDF hit Hamas positions including a factory that produces concrete for terror tunnels.
Parts of the town have been closed off and police bomb disposal units were at the scene of the strikes, a spokesman for the force said.
Following the strike, Hamas' Izzedine Al-Qassam Brigades announced that two of its members were killed in the strike, naming them as Ahmad Margan and Abdel Hafex Al-Silawi, both 23-years-old and from the Jabalia refugee camp.
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 escalation comes after the Hamas leadership convened for a rare meeting in Gaza on Friday.
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 footage was released by the Israeli Defence Force (IDF) and shows one rocket explode midair, but then a huge explosion causes mass panic and screams from school children.
The exchange came amid continued attempts by Egypt to broker a broad cease-fire deal between Israel and Hamas.