Beirut. Hamas said Thursday that it was sending a delegation to Egypt for further cease-fire talks, in a new sign of progress in attempts by international mediators to hammer out an agreement between Israel and the militant group to end the war in Gaza.

After months of stop-and-start negotiations, the cease-fire efforts appear to have reached a critical stage, with Egyptian and American mediators reporting signs of compromise in recent days. But chances for the deal remain entangled with the key question of whether Israel will accept an end to the war without reaching its stated goal of destroying Hamas.

The stakes in the cease-fire negotiations were made clear in a new UN report that said if the Israel-Hamas war stops today, it will still take until 2040 to rebuild all the homes that have been destroyed by nearly seven months of Israeli bombardment and ground offensives in Gaza. It warned that the impact of the damage to the economy will set back development for generations and will only get worse with every month fighting continues.

The proposal that US and Egyptian mediators have put to Hamas -- apparently with Israel’s acceptance -- sets out a three-stage process that would bring an immediate six-week cease-fire and partial release of Israeli hostages, but also negotiations over a “permanent calm” that includes some sort of Israeli withdrawal from Gaza, according to an Egyptian official. Hamas is seeking guarantees for a full Israeli withdrawal and a complete end to the war.

Hamas officials have sent mixed signals about the proposal in recent days. But on Thursday, its supreme leader, Ismail Haniyeh, said in a statement that he had spoken to Egypt’s intelligence chief and “stressed the positive spirit of the movement in studying the cease-fire proposal.”

The statement said that Hamas negotiators would travel to Cairo “to complete the ongoing discussions with the aim of working forward for an agreement.” Haniyeh said he had also spoken to the prime minister of Qatar, another key mediator in the process.

The brokers are hopeful that the deal will bring an end to a conflict that has killed more than 34,000 Palestinians, according to local health officials, caused widespread destruction and plunged the territory into a humanitarian crisis. They also hope a deal will avert an Israeli attack on Rafah, where more than half of Gaza’s 2.3 million people have sought shelter after fleeing battle zones elsewhere in the territory.

If Israel does agree to end the war in return for a full hostage release, it would be a major turnaround. Since Hamas’ Oct. 7 attack stunned Israel, its leaders have vowed not to stop their bombardment and ground offensives until the militant group is destroyed. They also say Israel must keep a military presence in Gaza and security control after the war to ensure Hamas doesn’t rebuild.

Publicly at least, Israeli Prime Minister Benjamin Netanyahu continues to insist that is the only acceptable endgame.

He has vowed that even if a cease-fire is reached, Israel will eventually attack Rafah, which he says is Hamas’ last stronghold in Gaza. He repeated his determination to do so in talks Wednesday with US Secretary of State Antony Blinken, who was in Israel on a regional tour to push the deal through.

The agreement’s immediate fate hinges on whether Hamas will accept uncertainty over the final phases to bring the initial six-week pause in fighting -- and at least postpone what it is feared would be a devastating assault on Rafah.

Egypt has been privately assuring Hamas that the deal will mean a total end to the war. But the Egyptian official said Hamas says the text’s language is too vague and wants it to specify a complete Israeli pullout from all of Gaza. The official spoke on condition of anonymity to talk about the internal deliberations.

On Wednesday evening, however, the news looked less positive as Osama Hamdan, a top Hamas official, expressed skepticism, saying the group’s initial position was “negative.” Speaking to Hezbollah’s Al-Manar TV, he said that talks were still ongoing but would stop if Israel invades Rafah.

Blinken hiked up pressure on Hamas to accept, saying Israel had made “very important” compromises.

“There’s no time for further haggling. The deal is there,” Blinken said Wednesday before leaving for the US.