Benjamin Netanyahu told US TV viewers: "If we don't win now, then Europe is next and you're next.
"We have to win to protect Israel. We have to win to safeguard the Middle East. We have to win for the sake of the civilised world.
"That's the battle we're fighting, and it's being waged right now. There is no substitute for that victory." As he spoke, world leaders called for Gaza's largest hospital to be protected as Israeli troops closed in.
The World Health Organisation says the Al-Shifa Hospital resembles a cemetery.
Doctors there told how around 200 patients had been buried in a mass grave.
People are dying because of a lack of medicine and power cuts are shutting down hospital equipment, they say.
Dr Adnan al-Bursh told the BBC that hospital staff spent six hours burying bodies in the hospital grounds while another 80 were still in the morgue.
The United Nations says dozens of babies and kidney patients can no longer be treated because of a lack of electricity.
US President Joe Biden told reporters at the White House: "It's my hope and expectation that there will be less intrusive action relative to the hospital.
"The hospital must be protected." PM Rishi Sunak also spoke of the "terrible suffering" of Palestinians in Gaza, saying too many civilians were dying.
While backing Israel's right to defend itself, he called for pauses in the fighting.
And a spokesman for UN secretary-general Antonio Guterres said he was "deeply disturbed by the horrible situation and dramatic loss of life in several hospitals in Gaza.
"In the name of humanity, the secretary general calls for an immediate humanitarian ceasefire."
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