The Hamas official reportedly said the truce agreement will begin with a two-week cease-fire trial period beginning in late August in accordance with ongoing talks mediated by Egypt. The Iron Dome aerial defense system intercepted 11 launches, the majority of the rockets hit open areas.
As alert sirens continued to go off in southern Israel, Hamas issued a statement saying "We are delivering on our promise".
"The Hamas terrorist organization is responsible for everything in and out of the Gaza Strip and will bear the consequences for the acts of terror perpetrated against Israeli civilians", the IDF said.
Katz, meanwhile, proposed "shifting the full responsibility over the Gaza Strip to the worldwide community, while keeping Israel's security control on port".
The strikes come in retaliation for a six-hour barrage of rockets which forced thousands of Israelis to seek shelter along Gaza border towns.
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".More news: Georgia Hall's dreams come true after famous Women's British Open triumph
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Israel's military earlier said shots were fired from Gaza at civilians working on the barrier that separate the territory and Israel, damaging a vehicle.
The incident capped a day of tension in the Gaza Belt region, a day after IDF tanks shelled a Hamas guardpost after mistaking a training exercise for aggression directed towards Israel.
Hamas warned Israel - with which it has fought three wars since 2008 - it would pay for the attack.
The Swedish government confirmed that all the Swedes had been sent home on Wednesday, while the Ship to Gaza activist group said shortly before midday that "most of [the activists] are already in transfer".
One Hamas militant was killed in the air strikes, as was a Palestinian woman and her 18 month old child, Palestinian officials said.
Israel has lost tracts of farmland and forest to fires started by kites and helium balloons laden with incendiary material which have caused fires in Israeli forests and farmlands and flown over the border by Palestinians in Gaza. He said by the end of the month, all fuel supplied by the United Nations will run out "and the problem is there is no sign of renewed funding from donors in the horizon".