JERUSALEM/GAZA/TEL AVIV, Oct 12 (Reuters) - Israel said on Thursday there would be no humanitarian exceptions to its siege of the Gaza Strip until all its hostages were freed, after the Red Cross pleaded for fuel to be allowed in to prevent overwhelmed hospitals from "turning into morgues".

U.S. Secretary of State Antony Blinken arriving in Tel Aviv on a trip to show solidarity, told Prime Minister Benjamin Netanyahu that America would always be by Israel's side.

Israel has vowed to annihilate the Hamas movement that rules the Gaza Strip, in retribution for the deadliest attack on civilians in Israeli history, when hundreds of gunmen crossed the barrier and rampaged through towns on Saturday.

Public broadcaster Kan said the Israeli death toll had risen to more than 1,300. Most were civilians gunned down in their homes, on the streets or at a dance party. Scores of Israeli and foreign hostages were taken back to Gaza; Israel says it has identified 97 of them.

Israel has responded so far by putting Gaza, home to 2.3 million people, under total siege and launching by far the most powerful bombing campaign in the 75-year history of the Israeli-Palestinian conflict, destroying whole neighbourhoods. Gaza authorities said more than 1,400 Palestinians have been killed and more than 6,000 have been wounded.

The International Committee of the Red Cross said fuel powering emergency generators at hospitals in Gaza could run out within hours.

"Without electricity, hospitals risk turning into morgues," ICRC regional director Fabrizio Carboni said. "The human misery caused by this escalation is abhorrent, and I implore the sides to reduce the suffering of civilians."

Israeli Energy Minister Israel Katz said there would be no exceptions to the siege without freedom for Israeli hostages.

"Humanitarian aid to Gaza? No electrical switch will be lifted, no water hydrant will be opened and no fuel truck will enter until the Israeli hostages are returned home. Humanitarian for humanitarian. And nobody should preach us morals," Katz posted on social media platform X.

Egypt, which has a single border crossing with Gaza, said it was trying to allow in aid there.

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Photo from Reuters