CAIRO — The United States stepped up pressure for a cease-fire deal in Gaza on Monday as the secretary of state said a new proposal had been put to Hamas, whose officials were in Cairo talking to Egyptian mediators. Israeli airstrikes killed 26 people in Gaza’s southernmost town of Rafah, according to hospital records.

U.S. Secretary of State Antony Blinken, ahead of a visit to Israel this week, urged Hamas to accept the latest proposal, calling it “extraordinarily generous” on Israel’s part.

The terms were not made public. But according to an Egyptian official and Israeli media, Israel has softened its position, lowering the number of hostages it demands that Hamas free during the initial six-week phase of the cease-fire in return for the release of hundreds of Palestinians from Israeli prisons.

One question is whether that will be enough to overcome Hamas concerns over the cease-fire’s second phase.

Hamas has demanded assurances that an eventual release of all hostages will 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 once it is over. The issue has repeatedly obstructed efforts by U.S., Egyptian and Qatari mediators during months of talks.

Israel’s closest ally, the United States, and others have repeatedly warned against an offensive on Rafah, saying it would bring a surge in casualties and worsen a humanitarian catastrophe. More than 1 million Palestinians have sought shelter in Rafah after fleeing fighting elsewhere.

Israel’s offensive in Gaza has killed more than 34,000 people.

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

Egypt has stepped up mediation efforts for a cease-fire deal in hopes of averting an assault on Rafah, on Gaza’s border with Egypt.

An Egyptian official said Israel has lowered the number of hostages it wants freed in the first stage, down from earlier demands for 40. He did not specify the new number. Israeli media said it now seeks the release of 33 hostages in return for the release of some 900 Palestinian prisoners. Hamas is believed to hold around 100 Israelis in Gaza.