CAIRO — Three days of negotiations with Hamas over a cease-fire in Gaza and the release of Israeli hostages failed to achieve a breakthrough on Tuesday, Egyptian officials said, less than a week before the start of the Muslim holy month of Ramadan, the informal deadline for a deal.

The nearly five months of fighting left much of Gaza in ruins and created a worsening humanitarian catastrophe, with many, especially in the devastated northern region, scrambling for food to survive.

“We must get more aid into Gaza,” U.S. President Joe Biden said Tuesday. “There’s no excuse. None.”

Aid groups have said it has become nearly impossible to deliver supplies within most of Gaza because of the difficulty of coordinating with the Israeli military, the ongoing hostilities and the breakdown of public order.

An Israeli army tank moves in the Gaza Strip, as seen from southern Israel on Tuesday. Leo Correa/Associated Press

The United States, Qatar and Egypt have spent weeks trying to broker an agreement in which Hamas would release up to 40 hostages in return for a six-week cease-fire, the release of some Palestinian prisoners and an major influx of aid to the isolated territory.

Two Egyptian officials said that the latest round of discussions ended on Tuesday. They said Hamas presented a proposal that mediators would discuss with Israel in the coming days. One of the officials said that mediators would meet Wednesday with the Hamas delegation, which didn’t leave Cairo.

Hamas has refused to release all of the estimated 100 hostages it holds, and the remains of around 30 more, unless Israel ends its offensive, withdraws from Gaza and releases a large number of Palestinian prisoners, including senior militants serving life sentences.

U.S. officials have said that they are skeptical that Hamas actually wants a deal, because the group has balked at a number of what the U.S. and others believe are legitimate requests, including giving the names of hostages to be released.

“It is on Hamas to make decisions about whether it is prepared to engage,” U.S. Secretary of State Antony Blinken said Tuesday.

“We have an opportunity for an immediate cease-fire that can bring hostages home, that can dramatically increase the amount of humanitarian aid getting in to Palestinians who so desperately need it, and can set the conditions for an enduring resolution,” Blinken said.

Senior Hamas official Osama Hamdan said Tuesday that his group demands a permanent cease-fire, rather than a six-week pause, and a “complete withdrawal” of Israeli forces.

“The security and safety of our people will be achieved only by a permanent cease-fire, the end of the aggression and the withdrawal from every inch of the Gaza Strip,” Hamdan told reporters in Beirut.

Israeli Prime Minister Benjamin Netanyahu has publicly rejected Hamas’ demands and repeatedly vowed to continue the war until Hamas is dismantled and all the hostages are returned. Israel didn’t send a delegation to the latest round of talks.

Israel was still waiting for Hamas to hand over a list of hostages who are alive as well as the hostage-to-prisoner ratio it seeks in any release deal, an Israeli official said. It wasn’t clear if that information was included in the latest proposal.

People gather at Israel’s Nitzana border crossing with Egypt in southern Israel on Tuesday, protesting against the delivery of humanitarian aid to the Gaza Strip until all hostages held by Hamas militants are released. Leo Correa/Associated Press

The Israeli and Egyptian officials spoke on condition of anonymity because they weren’t authorized to brief the media on the negotiations.

When asked whether Hamas has a list of the surviving hostages, Hamdan said that the matter wasn’t relevant to the talks and accused Israel of using it as an excuse to avoid engaging in the negotiations.

Benny Gantz, a member of Netanyahu’s War Cabinet and his main political rival, met with senior U.S. officials in Washington on a visit that drew a rebuke from the prime minister, the latest sign of a growing rift within Israel’s leadership.

Mediators had hoped to broker an agreement before Ramadan, the month of dawn-to-dusk fasting that often sees heightened Israeli-Palestinian tensions linked to access to a major holy site in Jerusalem. Ramadan is expected to begin around March 10, depending on the sighting of the moon.

“The negotiations are sensitive. I can’t say there is optimism or pessimism, but we haven’t yet reached a point at which we can achieve a cease-fire,” Egyptian Foreign Minister Sameh Shoukry said Monday.

The war began with a Hamas attack on southern Israel on Oct. 7 in which Palestinian militants killed around 1,200 people and took about 250 hostages. More than 100 of them were released during a weeklong cease-fire in November.

The attack sparked an Israeli invasion of the enclave of 2.3 million people that Gaza’s Health Ministry says has killed more than 30,000 Palestinians. Aid groups say the fighting has displaced most of the territory’s population and pushed a quarter of the population to the brink of famine.

The U.N. children’s agency said Monday that at least 10 children have reportedly died in isolated northern Gaza because of dehydration and malnutrition.

“There are likely more children fighting for their lives somewhere in one of Gaza’s few remaining hospitals, and likely even more children in the north unable to obtain care at all,” Adele Khodr, the UNICEF regional director for the Middle East and North Africa, said in a statement.

“These tragic and horrific deaths are man-made, predictable and entirely preventable,” she added.

The Gaza Health Ministry said Sunday that 15 children have starved to death at the Kamal Adwan Hospital in northern Gaza and another six were at risk of dying from malnutrition and dehydration. It wasn’t clear if the children had underlying medical conditions that increased their vulnerability.

Northern Gaza, the first target of Israel’s offensive, has suffered mass devastation. The World Food Program recently suspended aid shipments to the north, citing a security breakdown. An attempt by the Israeli military to bring in aid ended in tragedy last week when more than 100 Palestinians were fatally shot by Israeli forces or trampled to death in a melee.

The United States and Jordan airdropped 36,800 meals over northern Gaza on Tuesday, the second U.S. airdrop since Saturday.

Up to 300,000 Palestinians are believed to remain in northern Gaza after Israel ordered the evacuation of the entire region, including Gaza City, in October. Many have been reduced to eating animal fodder to survive. The U.N. says that one in six children under age 2 in the north suffer from acute malnutrition.

Israel is still carrying out strikes in all parts of Gaza. Gaza’s Health Ministry said that 97 people had been killed over the last 24 hours, bringing the overall Palestinian death toll to 30,631. The ministry doesn’t differentiate between civilians and combatants in its figures, but says women and children make up around two-thirds of the total casualties.

Tia Goldenberg reported from Tel Aviv, Israel, and Wafaa Shurafa from Rafah, Gaza Strip. Abby Sewell in Beirut, and Matthew Lee and Aamer Madhani in Washington, contributed to this report.