JERUSALEM — Claiming it had achieved most of its objectives and pressured by Western allies to stop causing civilian casualties in Gaza, Israel moved to wind down its operations there on Monday — either unilaterally or through a new Egyptian-brokered cease-fire announced late in the day.

The Egyptian proposal, which in principle was to start at 8 a.m. local time on Tuesday, was created “out of concern for innocent lives and to prevent further bloodshed,” and would initially last for 72 hours, an Egypt Foreign Ministry statement said. Both Israel and Hamas indicated they would respect the cease-fire, which would be followed by talks on a more lasting arrangement.

But given the history of broken cease-fires in the conflict, it was unclear that both sides would honor Egypt’s proposal, which was similar to one previously rejected by Hamas.

Earlier in the day, Israel appeared to be positioning itself to conclude its military operation in Gaza, with or without a formal cease-fire agreement.