A US-backed foundation tasked with supplying aid to Gaza made a faltering start Monday, with no clear sign that it had distributed promised supplies, a day after its chief unexpectedly stepped down.

The aid plan, which has been endorsed by Israel but rejected by the UN, is unfolding amid fierce Israeli attacks on the enclave, including on a school building where dozens of Palestinians sheltering inside were killed.

With food still critically short after a nearly three-month blockade, Washington says it is working to restore a ceasefire more than 19 months into the war, but progress is elusive.

A Palestinian official said Hamas had agreed to a US proposal for a truce and the release of 10 Israeli hostages, but an Israeli official dismissed the proposal as unacceptable, denying it was Washington's.

US special envoy Steve Witkoff rejected reports that Hamas had agreed to his proposal, telling Reuters that what he has seen is "completely unacceptable."

Israel has faced a mounting international outcry this month, including from Western allies, as it launched a new offensive in Gaza, already largely destroyed by Israeli bombardment and where the population of 2 million is at risk of famine.

Close ally Germany said Israel's recent attacks in The Gaza Humanitarian Foundation, which intends to use private contractors working under a broad Israeli security umbrella, said it would begin deliveries on Monday, with the aim of reaching one million Palestinians by the end of the week.

"We plan to scale up rapidly to serve the full population in the weeks ahead," it said in a statement.

Palestinians said they had seen no sign of any aid distribution by the new company.

The foundation's executive director, Jake Wood, announced his resignation on Sunday, saying it could not adhere "to the humanitarian principles of humanity, neutrality, impartiality, and independence".

Israeli strikes killed at least 45 people on Monday, local health authorities said.

In Gaza City, medics said, 30 Palestinians, including displaced women and children who were seeking shelter in a school, were killed in an airstrike.

Another strike on a house in Jabalia, adjacent to Gaza City, killed at least 15 other people, medics said.