Palestinian Hamas said it was "keen to reach a ceasefire" agreement but protested "new conditions" from Israel in the latest US proposal which Blinken said Israel had accepted.

The US secretary of state, on his ninth regional visit since the Israeli war on Gaza began more than 10 months ago, flew from Israel to Egypt on Tuesday for talks with President Abdel Fattah El-Sisi.

Sisi told Blinken that "the time has come to end the ongoing war", warning of the consequences of "the conflict expanding regionally", according to an official statement.

Blinken then travelled to Doha to meet with Qatari Emir Sheikh Tamim bin Hamad Al-Thani.

Both Egypt and Qatar are working alongside the United States to broker a truce, which diplomats say would help avert a wider conflagration that could draw in Iran and Hezbollah in Lebanon.

Israel and Hamas have blamed each other for delays in reaching an accord that would stop the Israeli assault, free Israeli captives and allow vital humanitarian aid into the besieged Palestinian territory.

One of the main sticking points has been Hamas's long-standing demand for a "complete" withdrawal of Israeli troops from all parts of Gaza, which Israel has rejected.

​'Crucial passage'

Mediators met last week with Israeli negotiators in Doha, and more truce talks are expected in Egypt this week.

Fears of a regional escalation have mounted since Hezbollah and Iran vowed to respond after an Israeli attack last month killed Hamas political leader Ismail Haniyeh in Tehran, shortly after an Israeli strike on Beirut killed top Hezbollah commander Fuad Shukr.

The powerful Lebanese group on Tuesday claimed a string of attacks on Israeli troops and positions.

Lebanon's health ministry said two people were killed in Israeli strikes in the country's south, in the latest of the cross-border exchanges which have raged almost daily since the Gaza war began.

Blinken said on Monday that there was "a real sense of urgency here, across the region", and called ongoing mediation efforts "probably the best, maybe the last, opportunity to get the hostages home, to get a ceasefire".

Hamas had called on the mediators to implement a framework set out by US President Joe Biden in late May, rather than hold more negotiations.

The Biden framework would freeze fighting for an initial six weeks while Israeli captives are exchanged for Palestinian prisoners in Israeli jails and humanitarian aid enters Gaza.

Hamas said on Sunday that the current US proposal, which Washington had put forward after two days of meetings in Doha, "responds to Netanyahu's conditions".

And on Monday, in response to comments by Biden that it was "backing away" from a deal, the Palestinian group said the "misleading claims... do not reflect the true position of the movement, which is keen to reach a ceasefire".

Hamas officials as well as some analysts and critics in Israel have accused Netanyahu of prolonging the war for political gain.

On the ground in Gaza, the United Nations said parts of a north-south Gaza road that is "a crucial passage for humanitarian missions were included in the latest evacuation order" issued by the Israeli military on Saturday.

"This has made it nearly impossible for aid workers to move along this key route", a statement said, preventing "critical supplies and services, such as water trucking" from reaching those in need.

Israel recovers dead captives

Israel's relentless bombardment and ground invasion have killed at least 40,173 Palestinians in Gaza, according to the territory's health ministry.

Most of the dead are women and children, according to the UN human rights office.

Out of the 251 captives seized during Hamas's October offensive against Israel, 105 are still being held in Gaza.

Israeli airstrikes on Gaza have resulted in the deaths of dozens of captives, including 34 confirmed dead by the Israeli military.

Despite these casualties, Israeli army operations in Gaza have continued throughout the truce talks.

An Israeli strike on Tuesday hit a school in Gaza City where the civil defence agency said at least 12 Palestinians were killed.

Thousands of displaced Palestinians had sought refuge in the facility, civil defence spokesman Mahmoud Bassal said.

AFP photos showed the Mustafa Hafiz school partly reduced to rubble, with Palestinians fleeing.

Elsewhere in Gaza, Bassal and medical sources reported at least 17 killed in four separate strikes.

The Israeli military claimed forces had retrieved the bodies of six captives from a tunnel in the southern Gaza district of Khan Younis.

Campaign group the Hostages and Missing Families Forum called on the government to "do everything in its power to finalise the deal currently on the table" and rescue the remaining captives.

*This story was edited by Ahram Online.