Israeli warplanes pounded Gaza for a fourth day on Monday, killing six more Palestinians, as a teenager died in a mystery blast, raising the death toll so far to 25.
Hamas officials said efforts mediated by Egypt to restore a ceasefire were continuing, but denied any breakthrough.
Israeli and Palestinian sources reported four air strikes on Monday evening, which Palestinian medics said left two people dead.
Islamic Jihad named the men as its members Bassam al-Ajla and Mohammed Dahir, and the Israeli military confirmed the raid, saying it targeted a "terrorist cell that was preparing to fire rockets."
The army also reported two more evening raids, one targeting "two rocket-launching sites" in northern Gaza and another against a "tunnel used by terrorists" under the border with Egypt.
And Palestinian sources reported a fourth strike in Beit Lahiya, in northern Gaza. There were no reports of injuries.
In a statement, Hamas prime minister Ismail Haniya said efforts by Egypt to broker a ceasefire were continuing, but Hamas sources said no truce deal had yet been reached.
"Efforts are continuing to protect our people, even though the road to restore the calm is difficult because of the continuing aggression, but we expect these efforts to succeed," Haniya said in a statement.
The violence continued throughout the day on Monday, with an Israeli air strike on the Jabaliya refugee camp in the northern Gaza Strip killing 65-year-Mohamed Mustafa al-Hasumi and his 35-year-old daughter Faiza, medics said, describing both as civilians.
The Israeli military said the strike targeted "a terrorist squad." It said the raid may have caused "the apparent injury of uninvolved persons," but described the incident as "a blatant example of how terror organisations use human shields to carry out terror attacks."
Earlier Monday, Islamic Jihad said two raids near the southern town of Khan Yunis had killed two of its members.
And Palestinian medics reported the death of a 15-year-old boy in what they described as a drone strike in the northern Gaza Strip, although the Israeli military denied any air force attacks in the area at the time.
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Militants fired a steady stream of rockets at towns and cities in southern Israel throughout Monday and Israeli Prime Minister Benjamin Netanyahu warned that the army could expand its operations if the fire continued.
"The Israeli army is prepared to expand its activities, and will continue its activities as long as necessary," he told MPs from his rightwing Likud party, hailing the Jewish state's "crushing offensive abilities."
Between midnight and 9 pm (2200 GMT Sunday and 1900 GMT Monday), Gaza militants fired 66 rockets and mortar rounds, the army said, of which 42 hit Israeli territory, and 24 were intercepted by the Iron Dome missile system.
More than 200 rockets have been fired at the Jewish state since the violence began on Friday, although the casualties have been minimal with just four people hurt over the weekend and a fifth injured on Monday.
In Gaza, medics put the death toll at 25, with at least 83 injured since the latest cycle of violence began with Israel's assassination of a senior militant.
Of those killed in Gaza, 19 were militants -- 12 from Islamic Jihad, and five from the Popular Resistance Committees -- and six were civilians, among them two minors.
The continuing violence prompted international concern, with US Secretary of State Hillary Clinton condemning the "rocket fire from Gaza by terrorists into southern Israel."
"We call on those responsible to take immediate action to stop these attacks. And we call on both sides, all sides, to make every effort to restore calm," she told the UN Security Council.
She later joined her counterparts from the European Union, Russia and the United Nations for a meeting of the so-called Middle East Quartet, which "expressed serious concern for the recent escalation."
"The Quartet reiterates its call on the parties to remain engaged and to refrain from provocative actions," a statement said.
The violence kicked off on Friday after Israel killed Zuhair al-Qaisi, head of the Popular Resistance Committees, prompting militant groups to begin lobbing rockets over the border.
The army said Qaisi had planned a deadly attack in August 2011 and accused him of planning a repeat attack "in the coming days."