A woman and children are in shock following the Israeli bombardment of Nuseirat in the central Gaza Strip on Monday. (AFP-Yonhap)

JERUSALEM -- Hopes rose Monday for a long sought-after cease-fire and hostage release deal after almost seven months of war in Gaza between Israel and Hamas.

Washington's top diplomat said he was "hopeful" Hamas would accept the offer, which his British counterpart said could see the release of thousands of Palestinian prisoners.

After meeting in Cairo, the Hamas delegation left Egypt and returned to Qatar "to discuss the ideas and the proposal ... and we are keen to respond as quickly as possible," a Hamas source close to the talks told Agence France-Presse on condition of anonymity.

According to Egyptian sources quoted by Al-Qahera News, a site also linked to Egyptian intelligence services, the Hamas delegation will "return with a written response to the truce proposal."

For months, mediators from Egypt, Qatar and the United States have been trying to broker a new agreement between the combatants. A one-week truce in November saw 80 Israeli hostages exchanged for 240 Palestinians held in Israeli prisons.

Diplomacy in the past few days appeared to suggest a new push to halt the fighting.

The war has brought Gaza to the brink of famine, United Nations and humanitarian aid groups say, while reducing much of the territory to rubble and raising fears of a wider regional conflict.

Salvaging belongings from the remains of a house in Gaza City, a bandage on his head, Ibrahim Juzar said a strike wounded his three girls and wife.

"My wife's chest has been fractured" and she has internal bleeding, he said.

US Secretary of State Antony Blinken told a World Economic Forum special meeting in Riyadh that the proposal before Hamas is "extraordinarily, extraordinarily generous on the part of Israel."

He urged the Islamist group to "decide quickly," saying, "I'm hopeful that they will make the right decision."

Blinken is on his seventh visit to the region since the Oct. 7 Hamas attack on Israel that sparked the current war.

Speaking at the WEF meeting, Egypt's Foreign Minister Sameh Shoukry said, "The proposal has taken into account the positions of both sides." "We are hopeful," he added.

British Foreign Secretary David Cameron told the same gathering that Hamas has been offered a "sustained 40 days' cease-fire, the release of potentially thousands of Palestinian prisoners, in return for the release of these hostages."

On the sidelines of the Riyadh meeting, European and Arab foreign ministers met to discuss how to join forces on advancing a two-state solution to the Israeli-Palestinian conflict.

Saudi Foreign Minister Prince Faisal bin Farhan is among the leaders who told the WEF gathering that tangible and irreversible steps towards establishing a Palestinian state would be an essential component of any deal for a durable cease-fire.

Israeli Prime Minister Benjamin Netanyahu is a long-standing opponent of Palestinian statehood.

In the Oct. 7 attack, militants seized hostages, 129 of whom Israel estimates remain in Gaza including 34 the military says are dead.

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

Israel's retaliatory offensive has killed at least 34,488 people in Gaza, mostly women and children, according to the territory's Health Ministry.

The tally includes at least 34 deaths in the past 24 hours, the ministry said. That is down from a peak this month of at least 153 deaths on April 9.

The majority of Gaza's 2.4 million people have sought refuge in Rafah near the border with Egypt.

To global alarm, Israel has vowed to carry out a ground invasion against Hamas in Rafah, but Foreign Minister Israel Katz said the government may "suspend" the invasion if an agreement is reached.

Medics and the Civil Defense Agency said at least 22 people were killed in the city. Witnesses told AFP at least three houses had been hit in strikes overnight from Sunday to Monday.

A crowd of grief-stricken relatives jostled over the dead, shrouded in white, at Rafah's Al-Najjar Hospital. Some women gently stroked the body bags holding the remains of their loved ones.

"We demand the entire world to call for a lasting truce. This is enough," a gray-haired relative who gave his name only as Abu Taha said at the hospital.

A Hamas source has told AFP the group is seeking a deal that "guarantees a permanent cease-fire, the free return of displaced people, an acceptable deal for (a prisoner-hostage) exchange and an end to the siege" in Gaza.

Israel has previously rejected a permanent cease-fire.

Protesters in Israel have demanded that the government reach an agreement to secure the release of the remaining hostages.

On Monday, the families of two Israeli captives seen alive in a video released by Hamas last weekend called for their release.

"I fear for Keith's life and I demand the leaders of the free world to help us bring our people home," said Aviva Siegel, who was freed in the November truce and is the wife of captive Keith Siegel, 64.

After an Israeli drone strike in early April killed seven workers from a US-based charity, US President Joe Biden suggested to Netanyahu, for the first time, that continued US support could be conditional on protection and aid for civilians.

On Sunday the White House said Israel is letting more aid trucks into Gaza in line with "commitments" Biden asked them to meet.

The UN has, however, continued to cite "access constraints" that it says significantly hinder efforts to reach the needy.

The US military is building a pier to help boost humanitarian supplies -- an effort that the Pentagon on Monday said will cost Washington at least $320 million.

The Gaza war has led to increased violence involving Iran's regional proxies and allies, including Yemen's Houthi rebels.

An Italian navy frigate on Monday shot down a drone in the Red Sea headed in the direction of an escorted merchant ship near the strategic Bab el-Mandeb Strait, Italy's Defense Ministry said. (AFP)