Diplomatic efforts intensified on Sunday to reach a long-sought truce and hostage-release deal in Gaza, as Hamas said it would travel to mediator Egypt to deliver its response after Israel's latest proposal.

The Israeli government has come under intense pressure from its global allies to reach a ceasefire, as well as from protesters within Israel demanding the release of hostages seized by Hamas militants during their October 7 attack that triggered the war.

A delegation from the Islamist movement will arrive in Egypt on Monday to deliver the group's response to Israel's new hostage and truce counterproposal, a senior Hamas official told AFP.

Egypt, Qatar, and the United States have been trying to mediate a new truce ever since a one-week halt to the fighting in November saw 80 Israeli hostages exchanged for 240 Palestinians held in Israeli prisons.

Hamas's unprecedented October attack resulted in the deaths of about 1,170 people in Israel, mostly civilians, according to an AFP tally of Israeli official figures.

Israel's retaliatory offensive against Hamas has killed at least 34,454 people in Gaza, mostly women and children, according to the health ministry in the Hamas-run territory.

Israel estimates that 129 hostages seized on October 7 are still being held in Gaza, including 34 the military says are dead.

Hamas has previously insisted on a permanent ceasefire -- a condition that Israel has rejected.

 'A complete failing' 

However, the Axios news website, citing two Israeli officials, reported that Israel's latest proposal includes a willingness to discuss the "restoration of sustainable calm" in Gaza after hostages are released.

It is the first time in the nearly seven-month war that Israeli leaders have suggested they are open to discussing an end to the war, Axios said.

A Hamas source close to the negotiations told AFP the group "is open to discussing the new proposal positively".

The source added that Hamas is "keen to reach an agreement that guarantees a permanent ceasefire, the free return of displaced people, an acceptable deal for (prisoner) exchange and ensuring an end to the siege" in Gaza.

Countries hoping to broker a ceasefire are among those attending a summit in Riyadh, where the kingdom's Foreign Minister Prince Faisal bin Farhan said the international community has failed Gaza.

"The situation in Gaza is a catastrophe by every measure –- humanitarian, but also a complete failing of the existing political system to deal with that crisis," Prince Faisal told the World Economic Forum (WEF) special meeting.

He reiterated that only "a credible, irreversible path to a Palestinian state" will prevent the world from confronting "this same situation two, three, four years down the line".

Israeli Prime Minister Benjamin Netanyahu's hard-right government rejects calls for a Palestinian state.

Palestinian president Mahmud Abbas, whose Palestinian Authority has partial administrative control in the Israeli-occupied West Bank, appealed at the WEF meeting for the United States to stop Israel from invading Rafah, which he said would be "the biggest disaster in the history of the Palestinian people".

Israel vows to go after Hamas battalions in southern Gaza City, but the prospect has raised global alarm because much of Gaza's population has sought shelter there, on the border with Egypt.

'Momentum' in truce talks

 US Secretary of State Antony Blinken, who backs steps towards a Palestinian state, is among the high-ranking global officials due to attend the Riyadh talks.

While there is no Israeli participation, the other key players will discuss the situation in Gaza, WEF president Borge Brende said.

There was "some new momentum now in the talks around the hostages, and also for... a possible way out of the impasse we are faced with in Gaza," he said.

Gaza's health ministry on Sunday reported at least 66 deaths in the past 24 hours, down from a peak this month of at least 153 deaths on April 9.

Israel carried out air strikes and shelling in Gaza overnight Saturday-Sunday, hitting three houses in the southern city of Khan Yunis, an AFP correspondent said, also reporting strikes on Gaza City and Rafah.

The Israeli military said its jets had struck dozens of targets including "launch sites, armed terrorists and observation posts".

On the side of a tent in Rafah on the weekend, a Palestinian wrote a message to the thousands of pro-Palestinian protesters on US university campuses.

"Thank you, students, in solidarity with Gaza, your message has reached," it read.

 Demonstrators push deal 

 In Israel, protesters have regularly taken to the streets, including at a heated rally in Tel Aviv late Saturday demanding that Netanyahu strike a deal that would free the hostages.

Hours earlier, Hamas released a video featuring two hostages, Keith Siegel and Omri Miran, who appeared to speak under duress.

"Keep protesting, so that there will be a deal now," Miran said in the footage.

"We are in danger here. There are bombs. It is stressful and scary," said Siegel, a 64-year-old US citizen.

United Nations humanitarian agency OCHA has warned that "famine thresholds in Gaza will be breached within the next six weeks" if a massive amount of food aid does not reach the territory.

At a market in Rafah, shoppers said fresh vegetables are selling at double or more their pre-war prices.

Mohammed Sarhan, 48, said 100 shekels used to buy enough for a week, but now they "are not enough for one meal for my family," forcing them to rely on aid and canned goods.

The White House said on Sunday that a US-made pier meant to boost aid to Gaza will become operational in two to three weeks but cannot replace land routes.

National Security Council spokesman John Kirby said on ABC News that Israel is letting in more trucks, in line with "commitments that President Biden asked them to meet".