Israel and Hamas on Monday gave cool public receptions to an Egyptian proposal to end their bitter war. But the two stopped short of rejecting the plan altogether, raising the possibility of a new round of diplomacy to halt a devastating Israeli offensive in the Gaza Strip.

The Egyptian plan calls for a phased hostage release and the formation of a Palestinian government of experts to administer the Gaza Strip and occupied West Bank, according to a senior Egyptian official and a European diplomat familiar with the proposal.

The Egyptian official, speaking on condition of anonymity to discuss the proposal, said the details were worked out with the Gulf nation of Qatar and presented to Israel, Hamas, the United States and European governments. Egypt and Qatar both mediate between Israel and Hamas, while the US is Israel’s closest ally and a key power in the region.

Israeli Prime Minister Benjamin Netanyahu did not comment directly on the proposal. But speaking to members of his Likud Party, he said he was determined to press ahead with Israel’s offensive.

"We are expanding the fight in the coming days and this will be a long battle and it isn’t close to finished,” he said.

A Palestinian mourns relatives killed in an overnight Israeli strike in Deir Al-Balah, Gaza, on Monday. AFP

Hamas has continued to fire rockets into Israel throughout the fighting. Late Monday, it launched a barrage of rockets, triggering air raid sirens in the southern city of Ashkelon. The media video showed what appeared to be several interceptions by Israel's rocket defence system. There were no immediate reports of damage or injuries.

The Egyptian proposal falls short of Israel’s declared goal of crushing Hamas. It also appears to be at odds with Israel’s insistence on maintaining military control over Gaza for an extended period after the war.

But Netanyahu faces heavy domestic pressure to reach a deal to bring home the more than 100 Israeli hostages who remain in captivity in Gaza.

As he vowed to continue the war during a speech in parliament, relatives of the hostages interrupted him and called for their immediate return. "Now! Now!” they shouted.

Women holding portraits of hostages wait for the war cabinet ministers in Tel Aviv on Monday. AFP

The rising death toll of Israeli soldiers from the ground operation also threatens to undermine public support for the war. The Israeli military announced the deaths of two more soldiers on Monday, bringing the total killed in the war to 156.

Netanyahu’s War Cabinet was expected to meet late on Monday. It was unclear if they would discuss the Egyptian proposal.

Associated Press