Israeli air strikes on Gaza killed three Palestinians on Sunday, raising the toll to 18, as Prime Minister Benjamin Netanyahu vowed no let-up against rocket-firing militants.
Hamas said it was talking with Egyptian officials in a bid to reach a truce with Israel, but warned that it expected the Jewish state to hold fire first and that talks had so far been unproductive.
And Islamic Jihad, which claimed responsibility for most of the rockets fired from Gaza in recent days, warned its operation would continue "whatever the price."
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.
Palestinian medics said 18 people had been killed in Israeli air strikes since Friday, and Israel said more than 120 rockets had landed in its territory, wounding four.
Both sides issued tough statements, with Netanyahu saying 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 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.
After more than 48 hours of fighting, 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.
Anyone who tries to harm Israeli citizens will face "severe consequences," he warned in a statement communicated by the military.
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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.
Medics named the other fatalities as 60-year-old Adel Saleh al-Issi and Ahmed Salim. They described Issi as a civilian but Salim's status was unclear.
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.
Since Friday, the Iron Dome air defence system set up around the southern cities of Ashdod, Ashkelon and Beersheva had intercepted 37 rockets, the army said.
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.
One hit a road in a residential neighbourhood, while a second landed next to a school, which was empty at the time because of a blanket closure imposed by the education ministry on schools within rocket range of Gaza, police said.
The rockets caused shrapnel damage to cars and buildings.
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 deadly 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.