Israeli war planes struck at the Gaza Strip and Palestinians fired more rockets against southern Israel on Monday in a fourth day of hostilities in which 25 Palestinians have been killed.
Egyptian efforts to broker a ceasefire appeared to be stuck over a demand by the Islamic Jihad militant group that Israel first promise not to target militant leaders for future attack.
The violence also drew condemnation from U.S. Secretary of State Hillary Clinton and United Nations Secretary-General Ban ki-Moon, who called for restraint. The Arab League also urged the United Nations to intervene to stop the conflict.
Twenty of the Palestinians killed since fighting flared in the Hamas-controlled enclave last Friday were militants and five were civilians, according to medical officials.
At least 80 Palestinians, mostly civilians, and eight people in Israel have been wounded.
The Israeli air strikes on Monday killed four Palestinian militants and an elderly man and his daughter, the officials said. The most recent attack came after nightfall, killing two militants near Gaza City, medics said.
A 15-year-old Palestinian youth died in an earlier explosion that Palestinians blamed on an Israeli missile. The Israeli military denied it had carried out a strike.
About 40 rockets, at least 20 of them intercepted by Israel's Iron Dome anti-missile system, were fired at Israel, wounding three people, Israeli police said. Three of these rockets struck in the city of Ashkelon just before the latest Israeli air strike.
Gaza's Hamas leadership, whose own cadres have kept out of the fighting, said on Sunday that neighbouring Egypt was working to stop the violence and consulting with other militants.
A Palestinian official close to the mediation told Reuters that Israel had agreed to a midnight ceasefire.
But Islamic Jihad, an Iranian-backed faction behind most of the rocket fire, said any truce should include an undertaking by Israel to end assassinations.
The exchanges began after two chiefs of the Popular Resistance Committees (PRC) faction, accused by Israel of planning to attack it through Egypt's Sinai desert, were killed in an Israeli strike on Friday.
Israel signalled that it would not halt what it calls preventive targeting operations aimed at stopping rocket fire and cross-border attacks.
The Israeli army will continue to attack the terrorists in Gaza with strength and determination, said Prime Minister Benjamin Netanyahu.
He also told members of his Likud party in parliament that the Israeli military was prepared to widen its operations and continue them for as long as necessary.
That prospect would revive memories of the 2008-2009 Gaza war in which about 1,400 Palestinians and 13 Israelis were killed.
But Israeli Interior Minister Eli Yishai said: Israel is not keen to see an escalation, Israel is not keen to hurt innocents, Israel is absolutely opposed to this.
For now, it is on this kind of scale. But if it will prove protracted, then without a doubt there will be a powerful, painful blow so that this will not continue, he told Army Radio.
The Palestinian attacks against Israel disrupted normal life in the south and forced many schools to close on Sunday and Monday. Alerts to residents of southern towns to take shelter from rockets punctuated radio programmes.
Israeli authorities said they planned to keep most of these schools shut also on Tuesday, and that a commercial crossing with Gaza, the territory's main trade and supply conduit from Egypt and Israel, would also be closed for the day.
Islamic Jihad and the PRC, armed groups largely independent of Islamist Hamas, have said they fired most of the scores of rockets launched at Israel since Friday.
Some experts in Gaza believe Hamas had provided some smaller groups with ammunition but avoided direct participation out of concern Israel would step up its attacks in the enclave.
Hamas is also eager to avoid any long-term military campaign as it struggles to adapt to political upheaval in Arab countries such as Egypt, which shares a border with Gaza, and in Syria, where the group has abandoned its traditional headquarters.
But efforts to negotiate a truce seemed elusive. Ibrahim Haniyeh, the Hamas leader in Gaza, blamed Israel's attacks.
In a statement on Tuesday evening Haniyeh said: Efforts are continuing to protect our people but the path to restoring calm is difficult because of the continued aggression.
Washington - Israel's principle ally - and the United Nations expressed concern at the violence.
Once again civilians are paying a terrible price, Ban told the U.N. Security Council. He denounced rocket attacks on Israel as unacceptable and urged Israel to exercise maximum restraint.
In her remarks to the council, Clinton condemned the rocket fire at Israel and urged both sides to restore calm. But she did not specifically mention the Israeli air strikes nor the dozens of Palestinian casualties.
France and Russia also both appealed for an end to the fighting and stressed the need to avoid civilian suffering.
Arab League Secretary-General Nabil al-Araby issued a statement in Cairo condemning the Israeli raids and urged the Security Council to step in and stop the aggression.
Gaza, home to 1.7 million people, was under Israeli occupation from 1967 until 2005 and remains under blockade.
Hamas has controlled Gaza since 2007 and is fighting for an independent Palestinian state but has shunned the stalled peace process supervised by international powers and refuses to recognise the Jewish state.
Islamic Jihad is less influential than Hamas but shares the same ideology, which advocates Israel's ultimate destruction.
(Writing by Allyn Fisher-Ilan, Dan Williams and Jeffrey Heller; Additional reporting by Cairo, U.N., Paris and Moscow bureaux; Editing by Angus MacSwan and David Stamp)