Israeli war planes carried out new air strikes on Gaza overnight, wounding 35, after Israel's premier vowed no let-up against rocket-firing militants.

Hamas emergency services spokesman Adham Abu Selmiya reported at least six air strikes across the Gaza Strip, including two in Jabalia refugee camp that left 33 people injured, "mostly children."

Two strikes hit east of Gaza City, injuring two, and two more raids hit open fields, one in Beit Lahiya in the north, and a second in central Khan Yunis.

An Israeli spokeswoman confirmed the strikes saying they "targeted a weapons storage facility and four rocket launching sites in the northern Gaza Strip, as well as a rocket launching site in the southern Gaza Strip."

The renewed strikes came after Israeli Prime Minister Benjamin Netanyahu warned raids would continue "as long as necessary" and Hamas officials said efforts to broker a ceasefire through Egypt were not bearing fruit.

Violence has spiked since Friday when Israeli jets raided the Gaza Strip, killing the head of a militant group and prompting barrages of rocket fire into the Jewish state.

On Sunday, the death toll in Gaza hit 18 and Israel said more than 120 rockets had landed in its territory, wounding four.

And Netanyahu warned that operations "will continue as long as necessary."

"I have given orders to strike all those who plan on attacking us," he said during a tour of southern Israel, public radio reported.

"The Israeli army has already dealt heavy blows to the terrorist organisations," he added.

Islamic Jihad, which has claimed responsibility for most of the rocket fire into Israel since Friday, quickly issued a statement in response, vowing that "operations will continue whatever the price."

"Escalation will be met with escalation, and what is coming is even greater," the group said.

Israel's top military officer said there would be no end in sight while rocket fire continued.

"The IDF (Israel Defence Force) has been responding, and will continue to do so with strength and determination against any firing of rockets at Israel," said Chief of Staff Lieutenant General Benny Gantz.

Both side called for action from the UN Security Council on Sunday, as the international peacemaking Quartet was to hold its first top-level meeting in six months on Monday.

Israel criticised international "silence" over rocket fire from Gaza, while the Palestinians accused the Jewish state of "crimes of aggression against the Palestinian people."

On Sunday, Israel carried out four air strikes killing three Palestinians, including 12-year-old Ayub Asaliya, killed on his way to school in Jabaliya refugee camp.

And Israel's defence ministry said Gaza militants had fired at least 124 rockets at the Jewish state since Friday, including 68 Qassams and 44 longer-range Grads, with Israel carrying out 26 air strikes on Gaza.

In Israel, four people were injured on Saturday, and several others were treated for shock after two Grads hit Beersheva on Sunday afternoon, medics said.

The violence erupted on Friday afternoon when an Israeli strike killed Zuhair al-Qaisi, the head of the militant Popular Resistance Committees group.

Additional strikes brought the death toll in Gaza to 15, including five PRC militants and 10 from Islamic Jihad, in the deadliest 24-hour period in and around Gaza in more than three years.

In response, armed groups lobbed a barrage of rockets into Israel, most of them claimed by Islamic Jihad's armed wing.

The Israeli army said Qaisi was involved in planning a deadly August 2011 attack in which militants sneaked across the border from Egypt's Sinai and killed eight in Israel's southern Negev desert.

And it said he was planning a similar attack "in the coming days."

The violence prompted concern from the United States and the European Union but there was no sign that a truce was on the horizon.

Hamas officials said on Sunday that intensive efforts were under way with Egypt to reach a mediated truce, but that they expected Israel to hold fire first.

"The Israeli aggression started this three days ago and before any talk about a truce, the Israeli side should stop," spokesman Taher al-Nunu told AFP.

[Image via Mikhail Levit /" target="_blank">]