Israel sent troops into a hospital in war-torn Gaza on Thursday where it said hostages may have been held, as medics warned the key medical facility was operating in "near impossible" conditions.

The raid came after days of intense fighting between troops and Hamas militants around the Nasser Hospital in Khan Yunis -- one of the largest medical sites in southern Gaza, and one of the territory's few hospitals that are still operational.

Israel, which has accused Hamas militants of using hospitals for military purposes, said it was carrying out a "precise and limited operation" at the facility with "no obligation" for patients or staff to evacuate.

Israeli army spokesman Daniel Hagari said there was "credible intelligence from a number of sources, including released hostages, indicating that Hamas held hostages at the Nasser Hospital in Khan Yunis and that there may be bodies of our hostages" there.

The health ministry in Hamas-ruled Gaza reported that thousands of people who had sought refuge in the complex, including patients, have been made to leave in recent days.

It has called the situation at Nasser "catastrophic", with staff unable to move bodies to the morgue because of the risks involved.

Medical charity Doctors Without Borders (MSF) described a "chaotic situation" in the hospital after it was shelled early Thursday, killing and wounding multiple people.

"Our medical staff have had to flee the hospital, leaving patients behind," MSF said, with one employee unaccounted for and another detained by Israeli forces.

The World Health Organization has described Nasser Hospital as a critical facility "for all of Gaza", where only a minority of hospitals are even partly operational.

- Gaza pounded -

Roughly 130 hostages are still believed to be in Gaza after the October 7 attack on Israel by Hamas militants, which resulted in the deaths of about 1,160 people, mostly civilians, according to an AFP tally based on official Israeli figures.

Dozens of the estimated 250 hostages seized during the attack were freed in exchange for Palestinian prisoners during a week-long truce in November. Israel says 30 of those still in Gaza are presumed dead.

At least 28,663 people, mostly women and children, have been killed in Israel's assault on the Palestinian territory, according to the health ministry.

Israel launched more deadly strikes on southern Gaza on Thursday after Prime Minister Benjamin Netanyahu insisted it would push ahead with a "powerful" operation in the overcrowded city of Rafah for "complete victory".

- 'No safe place' -

Hundreds of thousands of people have been driven into Rafah, seeking shelter in a sprawling makeshift encampment near the Egyptian border.

The city now hosts more than half of Gaza's population, with displaced people "crammed" into less than 20 percent of the territory, according to UN humanitarian agency OCHA.

"We were displaced from Gaza City to the south," said Ahlam Abu Assi. "(Then) they told us to go to Rafah, so we went to Rafah.

"We can't keep going and coming," she added. "There is no safe place for us."

US President Joe Biden warned Netanyahu by phone on Thursday against launching an operation in Rafah without a plan to keep civilians safe, the White House said.

Britain, meanwhile, joined Australia, Canada and New Zealand in warning Israel not to launch a ground offensive in the city.

Prime Minister Rishi Sunak told Netanyahu in a telephone call that Britain was "deeply concerned about... the potentially devastating humanitarian impact of a military incursion into Rafah," his office said.

In Cairo, efforts to secure a ceasefire entered a third day, with mediators from the United States, Qatar and Egypt trying to broker a deal to halt the fighting and see the release of the remaining hostages in exchange for Palestinian prisoners held by Israel.

CIA director Bill Burns made an unannounced visit to Israel on Thursday for talks with Netanyahu and the head of Israel's Mossad intelligence agency, David Barnea.

Barnea had already held talks with Burns and Egyptian and Qatari representatives in Cairo on Tuesday, before a Hamas delegation visited Wednesday.

US Secretary of State Antony Blinken said he believed an agreement was still "possible". "We're very focused on it and I believe it's possible," he said on a visit to Albania.

Families of the hostages protested outside the defence ministry in Tel Aviv to put pressure on the government to agree to a new prisoner exchange.

In one of the biggest demonstrations yet, some protesters handcuffed themselves to one another and also to ministry railings.

Biden told Netanyahu that the US was committed to "working tirelessly to support the release of all hostages".

- 'Drop delusional demands' -

Netanyahu's office said it had not received "any new proposal" from Hamas about releasing hostages, and Israeli media reported the country's delegation would not return to negotiations until Hamas had softened its stance.

While he did not comment directly on those reports, Netanyahu said: "I insist that Hamas drop their delusional demands and, when they drop these demands, we can move forward."

Palestinian president Mahmud Abbas, who heads the West Bank-based Palestinian Authority, has urged Hamas to "rapidly" agree to a truce and stave off further tragedy.

Netanyahu said late Thursday he rejected a plan for international recognition of a Palestinian state, following reports of the plan in The Washington Post.

With regional tensions high, Lebanon's Iran-backed Hezbollah movement said it had fired dozens of rockets into northern Israel, after Israeli strikes on Wednesday killed 15 people, including one of its commanders.

The Israeli military said it had killed Hezbollah commander Ali al-Debs, his deputy and another fighter.

Since the outbreak of the Israel-Hamas war, the Iran-backed Hezbollah movement has traded near-daily fire with Israeli troops, with tens of thousands displaced on both sides.