By Humeyra Pamuk and Nidal al-Mughrabi

CAIRO (Reuters) -U.S. Secretary of State Antony Blinken met Egyptian President Abdel Fattah El-Sisi in Cairo on Thursday as part of talks with Arab officials to seek a ceasefire in Gaza, after Israel's prime minister told U.S. Republicans there would be no let-up in the war against Hamas.

In Gaza itself, Israel's offensive focused on the Al Shifa hospital, the only partially working medical facility in the north of the Strip, for a fourth day, and local residents said they had seen buildings inside the complex in flames.

Five months of war have created critical food shortages among Gaza's 2.3 million Palestinians that in some areas now exceed famine levels, according to the United Nations.

"We’re pressing for an immediate ceasefire tied to the release of hostages," Blinken told the Arabic broadcaster Al Hadath. "That would bring immediate relief to so many people who are suffering in Gaza – the children, the women, the men."

He said the U.S. had drafted a resolution at the United Nations to that effect.

Ceasefire talks resumed this week in Qatar, centred on a truce of around six weeks that would allow the release of 40 Israeli hostages in return for hundreds of Palestinians detained in Israeli jails.

However, the main sticking point remains that Hamas says it will release hostages only as part of an agreement that would end the war, while Israel says it will discuss only a temporary pause.

"I think the gaps are narrowing, and I think an agreement is very much possible," Blinken told Al Hadath. "The Israeli team is present, has authority to reach an agreement."

Blinken and Sisi together reviewed progress in the talks, Sisi's office and the U.S. State Department said.

Sisi stressed the need for a truce to address the escalating humanitarian crisis and warned of the dangers of a military operation in Rafah, the last zone of relative safety for civilians where more than half the enclave's population is now sheltering, pressed against the Egyptian border.

As concern over starvation in Gaza mounts, officials from 36 countries and U.N. agencies gathered in Cyprus to discuss ways to expedite humanitarian deliveries.

One aid ship arrived in the enclave last week via a new route from Cyprus and two others are expected to depart soon, although aid agencies have said the shipments are logistically difficult and not nearly enough to replace food deliveries by truck.

"We have to remember there are limitations in terms of the reception and distribution," Cypriot Foreign Minister Constantinos Kombos said.

Near Al Shifa, residents told Reuters via a chat app that the army had blown up houses close by as buildings in the hospital complex burned.

Rabah, a father of five, said the area was a war zone, with people trapped inside their houses amid clashes in the streets.

"Israel sent tanks back into the heart of Gaza City to destroy what is left of its homes and roads. All of that is happening in the sight of the one-eyed world," he said.

ISRAEL SAYS MILITANTS HIDING IN HOSPITAL

Israel said its troops had killed more than 50 Hamas gunmen over the previous day, taking the number of fighters killed around the hospital to 140, along with two Israeli soldiers.

It said it had located terrorist infrastructure and weapons in and around the facility, showing images of AK-47 automatic rifles, rocket-propelled grenades, mortars and other artillery.

Military spokesperson Rear Admiral Daniel Hagari said "many Hamas terrorists - operatives and senior ones" had been hiding in the hospital along with Islamic Jihad militants.

"When we entered the hospital, we were finding terrorists fighting against us here in this area," he said.

Night-vision videos distributed by the Israeli military showed soldiers unloading boxes of food and water into the hospital.

Hamas has denied that the hospital harbours militants and said those killed were wounded patients and displaced persons.

Video footage released by Hamas showed its militants outside the Al Shifa compound, carrying weapons and firing on Israeli tanks in streets reduced to rubble. The position of the buildings and outline matched satellite imagery checked by Reuters.

Blinken was due to meet foreign ministers from Egypt, Saudi Arabia, Qatar and Jordan on Thursday, as well as the Emirati international cooperation minister and the general secretary of the Palestine Liberation Organization's (PLO) executive committee, the Egyptian foreign ministry said.

In his meeting with Saudi Arabia's crown prince on Wednesday, Blinken reaffirmed the U.S. commitment to the establishment of an independent Palestinian state with security guarantees for Israel.

The officials are pushing for an end to six months of fighting that has killed almost 32,000 Palestinians, with 65 killed in the previous 24 hours, according to Gaza health authorities.

The war was triggered by militants from Hamas, which controls Gaza, storming into southern Israel on Oct. 7, killing around 1,200 people and taking 253 hostages, by Israeli tallies.

Israeli Prime Minister Benjamin Netanyahu addressed U.S. Republican senators on Wednesday, telling them Israel would continue its efforts to defeat Hamas.

Israeli Strategic Affairs Minister Ron Dermer said on the "Call Me Back with Dan Senor" podcast that Israel would press on into Rafah, despite mounting international concern over the impact of such an offensive.

"It's going to happen. And it will happen even if Israel is forced to fight alone," he said.

"Even if the entire world turns on Israel, including the United States - we're going to fight until the battle's won."

(Reporting by Humeyra Pamuk and Nidal al-Mughrabi in Cairo; writing by Sharon Singleton; Editing by Kevin Liffey)