A delegation of the militant group Hamas was in Cairo on Saturday as Egyptian state media reported “noticeable progress” in ongoing cease-fire talks with Israel while an Israeli official downplayed the prospects for a full end to the war.

Pressure has been mounting to reach a deal — Gaza’s humanitarian crisis is dramatically escalating while Israel insists it will launch an offensive into Rafah, the territory’s southernmost city.

The stakes are high to find a halt to the nearly seven-month-long war. More than 1 million Palestinians are sheltering in the city of Rafah, along the border with Egypt, many having fled northern Gaza where a top U.N. official says there is now a full-blown famine.

Egyptian and American mediators have reported signs of compromise in recent days but chances for a cease-fire 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.

On Friday, CIA Director William Burns arrived in Cairo, Egypt, for the latest round of high-stakes negotiations over a hostage and cease-fire deal between Hamas and Israel, two U.S. officials and a source familiar with the matter told CBS News. 

The visit follows a stretch of technical talks and a fresh proposal from Israel that U.S. officials have described as “generous.”

Egyptian state Al-Qahera news said Saturday that a consensus has been reached over many of the disputed points but did not elaborate. Hamas has called for a complete end to the war and withdrawal of all Israeli forces from Gaza.

Earlier this week, Secretary of State Antony Blinken was back in Israel for his seventh visit to the country since Hamas militants staged their bloody Oct. 7 terrorist attack on the Jewish state, instantly sparking the war in the group’s Gaza Strip stronghold.

When he arrived, Blinken said the Biden administration was “determined” to see Hamas and Israel agree to a cease-fire in the conflict, which health officials in the Hamas-run Palestinian territory say has killed more than 34,000 people, most of them women and children. Desperate for more American support, Israelis rallied outside Blinken’s Tel Aviv hotel, some of them holding signs voicing hope that U.S. pressure will help bring home the remaining 133 hostages still thought to be held in Gaza, including five U.S. nationals still thought to be alive.

Meanwhile, the White House has urged Prime Minister Benjamin Netanyahu’s government to limit the scale of its operation in Rafah, and the head of the United Nations renewed his warning that a military offensive in the city would be “an unbearable escalation, killing thousands more civilians and forcing hundreds of thousands to flee.”   

The conflict erupted on Oct. 7, when Hamas attacked southern Israel, abducting about 250 people and killing around 1,200, mostly civilians. 

A senior Israeli official, speaking on condition of anonymity to discuss ongoing negotiations, played down the prospects for a full end to the war. The official said Israel was committed to the Rafah invasion and told The Associated Press that it will not agree in any circumstance to end the war as part of a deal to release hostages.

A strike in the Nuseirat refugee camp in central Gaza killed three people, according to hospital officials.

In the last 24 hours, the bodies of 32 people killed by Israeli strikes have been brought to local hospitals, Gaza’s Health Ministry said Saturday. The ministry does not distinguish between fighters and civilians in its tallies, but says that women and children make up around two-thirds of those killed.

The Israeli military says it has killed 13,000 militants, without providing evidence to back up the claim. It has also conducted mass arrests during its raids inside Gaza.

Gaza’s Health Ministry also on Saturday urged the International Criminal Court to investigate the death in Israeli custody of a Gaza surgeon. Adnan al-Borsh, 50, was working at al-Awda Hospital when Israeli troops stormed it, detaining him and others inside in December, according to the Palestinian Prisoner’s Club.

In related developments this week, Israel briefed Biden administration officials on plans to evacuate civilians ahead of the Rafah operation, according to U.S. officials familiar with the talks.

The United Nations has warned that hundreds of thousands would be “at imminent risk of death” if Israel moves forward into the densely packed city, which is also a critical entry point for humanitarian aid.

The U.S. director of the U.N. World Food Program, Cindy McCain, said Friday that trapped civilians in the north, the most cut-off part of Gaza, have plunged into famine. McCain said a cease-fire and a greatly increased flow of aid through land and sea routes was essential.

Israel recently opened new crossings for aid into northern Gaza, but on Wednesday, Israeli settlers blocked the first convoy before it crossed into the besieged enclave. Once inside Gaza, the convoy was commandeered by Hamas militants, before U.N. officials reclaimed it.

The proposal that Egyptian mediators had put to Hamas sets out a three-stage process that would bring an immediate, six-week cease-fire and partial release of Israeli hostages, and would include some sort of Israeli pullout. The initial stage would last for 40 days.

Hamas would start by releasing female civilian hostages in exchange for Palestinian prisoners held by Israel.

Gershon Baskin, director for the Middle East at the International Communities Organization, said it appears that Hamas has agreed to the framework that Egypt proposed and Israel has already accepted.

He said the negotiators are now hammering out the details — and if Israel sends its top negotiators to Cairo after the Sabbath ends on Saturday evening, that would signify it’s very serious.

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Jeffery reported from Jerusalem. Associated Press writers Josef Federman in Jerusalem and Bassem Mroue in Beirut contributed to this report.