STORY: There was cheering in Rafah in Gaza on Monday night after Hamas said it had accepted a ceasefire proposal from mediators, even as residents fled the city in fear of an Israeli assault.

But any likelihood of such a ceasefire taking place was quickly played down by Israel.

Hamas said in a brief statement that its chief had informed Qatari and Egyptian mediators that the group accepted their proposal for a ceasefire.

It comes as Israeli forces struck Rafah and ordered residents out of parts of the city, which has served as the last refuge for more than a million displaced Gazans.

A spokesperson for the Israeli military said all proposals that would release hostages held in Gaza would be considered...

But said that for now, its operations would continue.

In Tel Aviv, families of hostages kidnapped by Hamas in the October 7 attack called on President Benjamin Netanyahu to take the deal.

"Save lives. Don't talk about fighting and blood."

An Israeli official, speaking on condition of anonymity, said the proposal that Hamas had accepted was a watered-down version of an Egyptian offer and included elements that Israel could not accept.

An official briefed on the peace talks, also speaking on condition of anonymity, said however that the offer was effectively the same as one Israel had agreed to at the end of April.

Israel said on Monday it was conducting limited operations in part of Rafah, following a rocket attack that killed four Israeli soldiers the day before.

Omar Shakir with Human Rights Watch said an invasion of Rafah would be (quote) "unlawful and catastrophic."

"The areas that have been marked for evacuation are areas that have been decimated by Israeli forces, that do not have the infrastructure needed for human life."

A spokesperson for the U.S. State Department said Washington would discuss the Hamas response with its allies.

"It would bring an immediate cease-fire. It would allow increased movement of humanitarian assistance. And so we're going to continue to work to try to reach one."