More than five weeks into the war sparked by bloody attacks on Israel, Prime Minister Benjamin Netanyahu told US media "there could be" a deal to free some of the roughly 240 hostages seized by Palestinian militants on October 7 and believed held in Gaza.

But the Israeli premier, facing increasing pressure at home over the captives, stopped short of providing any details.

"The less I say about it, the more I'll increase the chances that it materializes," he told NBC.

In Gaza City, Al-Shifa hospital is caught in Israel's ground offensive aimed at destroying Hamas, and the compound has been repeatedly hit by strikes, one of which Hamas health officials said destroyed the cardiac ward on Sunday.

The Israeli military has denied deliberately targeting hospitals and has accused the Islamist militant group of using medical facilities or tunnels underneath them as hideouts -- a charge Hamas denies.

Fears intensified for Palestinians seeking shelter and patients needing treatment after Gaza City's Al-Quds hospital went out of service due to lack of generator fuel, the Palestinian Red Crescent said.

The bloodiest ever Gaza war broke out after Hamas fighters poured through the militarized border with Israel on October 7, killing around 1,200 people, mostly civilians, and taking about 240 people hostage, according to Israeli figures.

Israel's relentless campaign in response has killed at least 11,180 people in Gaza, also mostly civilians and including 4,609 children, according to the Hamas government's media office.

Despite growing calls for a ceasefire, Netanyahu has flatly rejected halting the fighting without release of the hostages.

White House National Security Council spokesman John Kirby told MSNBC there has been "active negotiation" on a potential deal but kept mum on any details, while a Palestinian official in Gaza accused Israel of dragging its feet.

"Netanyahu is responsible for the delay and obstacles in reaching a preliminary agreement on the release of several prisoners," the official told AFP on condition of anonymity.

Hospital in 'dire' state

Witnesses at Al-Shifa hospital told AFP by phone on Sunday that "violent fighting" had raged around the hospital the whole night.

Inside, doctors said Saturday that two babies had died in the neonatal unit after power to their incubators was cut off, and a man had also died when his ventilator shut down.

Youssef Abu Rish, deputy health minister in the Hamas government, reported on Sunday the deaths of three more premature babies and six other patients in critical condition.

"We fear the toll will rise further by morning," he said.

A "safe passage" was to be opened from Al-Shifa to allow people to flee toward the south, the Israeli military said Sunday.

The World Health Organization (WHO) said the situation inside Al-Shifa was "dire and perilous" and it was "not functioning as a hospital anymore".

"It's been three days without electricity, without water and with very poor internet which has severely impacted our ability to provide essential care," said WHO director Tedros Adhanom Ghebreyesus on X, formerly Twitter, after the agency was able to get in touch with Al-Shifa medical staff.

"Tragically, the number of patient fatalities has increased significantly," he said, urging a ceasefire "now".

Twenty of Gaza's 36 hospitals are "no longer functioning", according to the UN's humanitarian agency.

EU foreign policy chief Josep Borrell condemned Hamas for using "hospitals and civilians as human shields" in Gaza, while also urging Israel to show "maximum restraint".

Very little aid has made it into Gaza during the war, with the densely populated coastal territory effectively sealed off by a total blockade that Israel has vowed to maintain until the hostages are freed.

Only a handful of trucks carrying fuel had been let into Gaza since October 7, with Israel concerned fuel deliveries would be used by Hamas militants.

The Israeli army shared footage of troops leaving jerry cans of fuel outside Al-Shifa, in a video AFP was unable to independently verify.

Military spokesman Daniel Hagari said on Sunday Hamas authorities were preventing hospital staff from collecting the badly needed supply, while Al-Shifa director Mohammad Abu Salmiya told journalists the Israeli claims were "lies".

The 300 liters the army said had been delivered would power generators for "no more than quarter of an hour" anyway, Abu Salmiya said.

Fleeing south

As fighting raged, around 800 foreigners and dual nationals, as well as several wounded Palestinians, were evacuated from the besieged Gaza Strip to Egypt on Sunday, a Gaza border official said.

Rafah is the only crossing out of Gaza not controlled by Israel, and had been closed on Friday and Saturday.

Since November 1, dozens of wounded Palestinians have been evacuated to Egyptian hospitals, with hundreds of dual nationals and foreigners also leaving through Rafah.

Perched on trucks, crammed in cars, pulled by donkeys on carts and on foot, many thousands of Palestinians have fled Israeli army strikes on the territory squeezed between Israel, Egypt and the Mediterranean.

Almost 1.6 million people -- about two-thirds of Gaza's population -- have been internally displaced since October 7, according to the UN agency for Palestinian refugees UNRWA.

Strikes were also hitting buildings at the southern end of Gaza in Rafah, the area to which civilians have been urged to evacuate.

A strike in southern Bani Suheila destroyed a dozen houses on Sunday, killing at least four people and wounding at least 30, said an AFP reporter at the scene.

The International Committee of the Red Cross (ICRC) urged in a statement "the protection of civilians in Gaza trapped in fighting".

"People call us day and night, saying they are afraid to open their door for fear of getting killed," said William Schomburg, head of the ICRC mission in the territory.

The conflict has been stoking regional tensions and fears of the war expanding.

Returning from a summit in the Saudi capital Riyadh, which condemned Israeli forces' offensive in Gaza, Turkish President Recep Tayyip Erdogan called for pressure on the United States to stop the war.

"The West should increase pressure on Israel... It's vital for us to secure a ceasefire," he told reporters.

Israel's top ally Washington has offered some criticism of the civilian toll but has voiced support for the offensive and opposed a ceasefire.

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