An announcement by Hamas late Monday that it had accepted a cease-fire proposal sent people in the streets of Rafah into temporary jubilation, as Palestinian evacuees in the jam-packed town felt their first glimmer of hope the war could end.

For families of Israeli hostages held in Gaza, the announcement raised the possibility that their long wait was coming to an end — that they might soon see their loved ones.

But the fervor was short-lived.

A few hours after Hamas’ announcement, Israel rejected the proposal — which was different from one the two sides had been discussing for days — and said it was sending a team of negotiators for a new round of talks.