Israel launched a spate of air strikes on Gaza Monday killing two Palestinians, medics said, after Premier Benjamin Netanyahu vowed no let-up against rocket-firing militants.

Palestinian medics reported six air strikes in the early hours of Monday, which injured 35, and another two raids around the city of Khan Yunis around 0500 GMT, which left two dead and two injured.

The killings brought to 20 the death toll in Gaza in three days of tit-for-tat violence that began with Israel's killing of a senior militant on Friday.

Medics named the latest fatalities as 24-year-old Suleiman Abu-Mutlaq, killed east of Khan Yunis, and 24-year-old Raafat Jawad Abu-Eid, killed on a motorbike south of the city. There was no immediate information on whether they were civilians or militants.

The Israeli army had no immediate comment on the latest reported raids, but earlier confirmed it carried out six strikes that "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."

Israeli police spokesman Micky Rosenfeld said militants had fired 11 rockets into Israel overnight, including one that damaged a building in a kibbutz near the Gaza border. There were no injuries.

The exchange of fire, which followed tough words from Prime Minister Netanyahu and militants in Gaza on Sunday, suggested efforts by Hamas to broker a ceasefire through Egypt had yet to bear fruit.

On Sunday, Netanyahu warned that operations would "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 Forces) 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.

Violence has spiked since Friday when Israeli jets raided the Gaza Strip, killing Zuhair Al-Qaisi, the head of the Popular Resistance Committees militant group, and prompting barrages of Palestinian rocket fire into the Jewish state.