The United States has stepped up pressure for a ceasefire deal in Gaza as the secretary of state said a new proposal had been put to Hamas, whose officials were in Cairo talking to Egyptian mediators.

It came as Israeli air strikes killed 26 people in Gaza’s southern town of Rafah, according to hospital records.

US secretary of state Antony Blinken, ahead of a new visit to Israel this week, pressured Hamas to accept the latest proposal, calling it “extraordinarily generous” on the part of Israel.

Terms of the proposal were not made public, and it was not known if anything had changed on the main roadblock that US, Egyptian and Qatari mediators have repeatedly crashed against: the question of the extent of a ceasefire.

During months of talks, mediators have often signalled major progress only to come out empty-handed.

Hamas demands that the release of all hostages bring a complete end to Israel’s nearly seven-month assault in Gaza and a withdrawal of its troops from the devastated territory. Israel has offered only an extended pause, vowing to resume its offensive to destroy Hamas once the pause is over.

Israel says it plans to invade Rafah, Gaza’s southernmost town where more than one million Palestinians have sought shelter from fighting elsewhere.

Its closest ally, the United States, and others have repeatedly warned against it, saying an offensive would cause a new surge in mass casualties in a war that has already killed more than 34,000 people.

Overnight and Monday morning, Israeli strikes flattened at least three homes where extended families of Palestinians were gathered, and the dead included nine women and six children, one of whom was just five days old, according to hospital records and an Associated Press reporter.

“Everyone was sleeping in their beds,” said Mahmoud Abu Taha, whose cousin was killed with his wife and their year-old baby in one house where at least 10 died. “They have nothing to do with anything, all of them are girls and women.”

Egypt has stepped up mediation efforts for a ceasefire deal in hopes of averting an Israeli ground assault on Rafah, which sits on Gaza’s border with Egypt.

A Hamas delegation was in Cairo on Monday for talks over the new proposal.

Talks have centred on a two-phase deal that would bring an initial halt in fighting with the release of some of the around 100 hostages Hamas is believed to still hold in return for the freeing of Palestinians imprisoned by Israel, while talks are held for a second phase for the release of the rest, including soldiers.

An Egyptian official said Israel has lowered the number of hostages it wants freed in the first stage, down from its earlier demands for 40, though he did not specify the new number.

Israel has also shown flexibility on allowing residents to return to northern Gaza, he said.

The official said the Israelis “showed willingness” to discuss establishing a sustainable ceasefire in Gaza as part of the second phase of the deal.

“They showed willingness (to discuss it) but not commitment,” he said.

There was no immediate comment from Hamas or Israeli officials.

Israeli Prime Minister Benjamin Netanyahu has repeatedly rejected Hamas demands for an end to the war and a troop withdrawal and says an offensive on Rafah is crucial to destroying the militants after their October 7 attacks on Israel that triggered the war.

His government could also be threatened if he agrees to a deal, since hardline members of his Cabinet demand an attack on Rafah.

At the same time, Mr Netanyahu faces pressure from the families of hostages still in captivity who are demanding a deal for their release.

On Monday, the families of two hostages – Keith Siegel and Omri Miran – urged both sides to reach an agreement, days after Hamas released a video showing the two men.

Israeli officials, meanwhile, appeared increasingly concerned that the International Criminal Court (ICC) may issue arrest warrants against the country’s leaders.

It was not clear what sparked the Israeli concerns. The ICC launched a probe three years ago into possible war crimes committed by Israel and Palestinian militants going back to the 2014 Israel-Hamas war.

The probe is also looking at Israel’s construction of settlements in occupied territory the Palestinians want for a future state.

There was no comment from the court on Monday, and it has given no indication warrants in the case are imminent.

But Israel’s Foreign Ministry said late Sunday that it had informed Israeli missions of “rumours” that warrants might be issued against senior political and military officials.

Mr Netanyahu said on Friday that Israel “will never accept any attempt by the ICC to undermine its inherent right of self-defence”.

Neither Israel nor the United States accept the ICC’s jurisdiction, but any warrants could put Israeli officials at risk of arrest in other countries. They would also serve as a major rebuke of Israel’s actions at a time when pro-Palestinian protests have spread across US college campuses.

The International Court of Justice, a separate body, is investigating whether Israel has committed acts of genocide in the ongoing war in Gaza, with any ruling expected to take years. Israel has rejected allegations of wrongdoing and accused both international courts of bias.

In the Hamas-led attack on October 7 that triggered the war, militants stormed through army bases and farming communities across southern Israel, killing some 1,200 people, mostly civilians, and taking around 250 hostages.

Israel’s massive air, sea and ground offensive in Gaza has killed at least 34,488 Palestinians, mostly women and children, according to Gaza’s Health Ministry, which does not distinguish between civilians and combatants in its tally.

Israel blames the high civilian death toll on Hamas because the militants fight from dense, residential areas. The military says it has killed more than 12,000 militants, without providing evidence.

The war has driven around 80% of Gaza’s population of 2.3 million from their homes, caused vast destruction in several towns and cities, and pushed northern Gaza to the brink of famine.

Meanwhile, Mr Blinken said on Monday that Israel must still do more to increase the flow of humanitarian aid into the besieged Gaza Strip and that he would use his Middle East trip – his seventh to the region since the Israel-Hamas war started in October – to press that case with Israeli leaders.

Speaking at events in Saudi Arabia’s capital, Mr Blinken said the best way to ease the humanitarian catastrophe in Gaza would be to conclude an elusive ceasefire agreement, which also would release Israeli hostages held by Hamas.

He said safety for humanitarian relief workers must be improved and that there is a focus on ensuring the aid is making a proper impact for Palestinian civilians.

Scores of relief workers have been killed since the conflict began, and an Israeli attack on a World Central Kitchen convoy in Gaza this month that killed seven aid workers only highlighted the dangers and difficulties of protecting them. Israel has said the strike was a mistake and has disciplined officials involved.

World Central Kitchen said it would resume operations in Gaza on Monday after a four-week suspension.