Negotiations for a potential hostage deal and truce in Gaza appeared to reach a critical moment Saturday, with Hamas set to offer its response to the latest proposal, and Israel indicating an offensive in the city of Rafah could be imminent if no agreement is reached.

With Arab and American mediators pressing intensely for a temporary ceasefire, several reports Saturday said Hamas was prepared to accept the latest proposal, in light of assurances from the United States that there will be a “sustainable cessation” of the war.

It was not clear whether such a response would be a straightforward approval of the proposal on offer, or one that comes with various caveats.

A Hamas delegation was in Cairo Saturday, as was CIA Director William Burns, for meetings with Egyptian mediators.

The truce deal is believed to be composed of several potential phases, with the first phase seeing a limited release of “humanitarian” hostages for a truce of several weeks, while further phases featuring further releases and a more solid ceasefire are possible.

Citing unidentified sources, the Palestinian Al-Quds newspaper said American mediators had promised that Israel would completely withdraw from Gaza under the third and final phase, and the war would effectively end.

An unnamed Hamas source gave a similar statement to Israel’s Channel 12 news.

Hamas, Al-Quds reported, was for the first time poised to agree to launch the first phase without a guarantee of the war’s end, based on those assurances and its belief that it still holds significant cards in the form of hostages who will not be released under the first phase.

In response to the reports, an Israeli official, speaking anonymously to the media, repeated Jerusalem’s insistence that “Israel will under no circumstances agree to end the war as part of an agreement to free our abductees.”

The official added: “The IDF will enter Rafah and destroy the remaining Hamas battalions there — whether there is a temporary pause to free our captives or not.”

Signaling discord within Israeli leadership, war cabinet minister Benny Gantz criticized those comments.

“I advise the ‘official sources’ and all other decision-makers to wait for official updates, to act with restraint and not to become hysterical due to political reasons,” he said in a statement, apparently referencing far-right pressure on Prime Minister Benjamin Netanyahu not to agree to a deal that could be perceived as a win for Hamas.

Gantz added that when Hamas does submit a response, the war cabinet will convene to deliberate it.

Saudi newspaper Asharq also reported that an agreement was close and echoed that Hamas would announce its response to the proposal “in the coming hours.”

The Palestinian, Saudi and Channel 12 reports all said that the US had guaranteed Israel will withdraw all troops from Gaza upon completion of the third phase of the agreement. None of the reports included comments from US officials.

The Wall Street Journal reported Friday that Israel had given Hamas one week to agree to the hostage deal on the table, or it would launch its long-pledged offensive in Gaza’s southernmost city.

The latest proposal for the hostage deal reportedly includes a first phase lasting up to 40 days, in which at least 33 of 128 hostages held in Gaza would be released, along with an IDF withdrawal from parts of the Strip.

The first phase would allow for the return of Palestinians to northern Gaza and the release of hundreds of Palestinian security prisoners in exchange for hostages.

The potential second phase would last for 42 days and see the release of all other living hostages and the sides completing arrangements for sustainable calm in Gaza.

The third and final phase, which would see an exchange of bodies, would also last 42 days.

The Hamas source quoted by Channel 12 said “compromises were reached” regarding the number of Palestinian security prisoners to be released in exchange for each Israeli hostage.

The issue of allowing the import of “dual-use” items into the Strip — supplies that Israel fears could also be used for military purposes — was still being ironed out, the Hamas source added.

Despite the Israeli official’s comments, some Egyptian and Palestinian officials sounded cautious optimism.

“The results today will be different. We have reached an agreement over many points, and a few points remain,” one Egyptian security source told Reuters.

An unnamed Palestinian official with knowledge of the mediation efforts said that “things look better this time, but whether an agreement is on hand would depend on whether Israel has offered what it takes for that to happen.”

Egyptian media on Saturday reported “noticeable progress” in talks to secure a deal. A consensus has been reached over many of the disputed points, the Egyptian Al-Qahera news reported, without elaborating.

Talks have continued for months without a decisive breakthrough. Israel has said it is determined to eliminate Hamas, while Hamas says it wants a permanent ceasefire and a full Israeli withdrawal from the Gaza Strip. The Biden administration has said Hamas is the only party standing in the way of a deal.

On Friday, the Axios news site quoted senior Israeli officials who said they saw “early indications” that Hamas could agree to the first stage of the Egyptian-crafted, Israeli-backed proposal for a deal — involving the release of women, children, the elderly and the sick — even without an Israeli commitment to end the war, but with fewer hostages to be freed in exchange for more Palestinian security prisoners.

If so, the Israeli officials expect Hamas to set stricter requirements that could lower the number of hostages it will agree to release on so-called “humanitarian” grounds, and increase the number of Palestinian security prisoners to be freed in return, the news site said.

Israel is seeking the release of 33 female, elderly and sick hostages during the six-week first stage of the truce, but Hamas may only agree to release 20 hostages in those categories, according to the report.

Netanyahu has been threatening to enter Rafah for months, claiming repeatedly during that period that an invasion was imminent.