CAIRO -- Hamas said Saturday it was reviewing a new Israeli proposal for a cease-fire in Gaza, as Egypt intensified efforts to broker a deal to end the monthslong war and stave off a planned Israeli ground offensive into the southern Gaza Strip city of Rafah.

Senior Hamas official Khalil al-Hayya gave no details of Israel's offer, but said it was in response to a Hamas proposal two weeks ago. Negotiations earlier this month centered on a six-week cease-fire proposal and the release of 40 civilian and sick hostages in exchange for freeing hundreds of Palestinian prisoners in Israeli jails.

A separate Hamas statement said leaders from the three main militant groups active in Gaza discussed attempts to end the war.

The statements came hours after an Egyptian delegation ended a visit to Israel where it discussed a “new vision” for a prolonged cease-fire in Gaza, according to an Egyptian official, who spoke on condition of anonymity to freely discuss the developments.

The discussions between Egyptian and Israeli officials focused on the first stage of a plan that would include a limited exchange of hostages held by Hamas for Palestinian prisoners, and the return of a significant number of displaced Palestinians to their homes in northern Gaza “with minimum restrictions,” the Egyptian official said.

Mediators are working on a compromise that will answer most of both parties’ main demands, which could pave the way to continued negotiations with the goal of a deal to end the war, the official said.

Hamas has said it won’t back down from demands for a permanent cease-fire and full withdrawal of Israeli troops. Israel has rejected both and said it will continue military operations until Hamas is defeated and that it will retain a security presence in Gaza.

There is growing international pressure for Hamas and Israel to reach a cease-fire deal and avert an Israeli attack on Rafah, where more than half of Gaza’s 2.3 million people have sought refuge.

Israel has insisted for months it plans a ground offensive into Rafah, on the border with Egypt, where it says many remaining Hamas militants remain, despite calls for restraint including from Israel’s staunchest ally, the United States.

Egypt has cautioned an offensive into Rafah could have “catastrophic consequences” on the humanitarian situation in Gaza, where famine is feared, and on regional peace and security.

The Israeli military has massed dozens of tanks and armored vehicles in southern Israel close to Rafah and hit locations in the city in near-daily airstrikes.

Early Saturday, an airstrike hit a house in Rafah’s Tel Sultan neighborhood, killing a man, his wife and their sons, ages 12, 10 and 8, according to records of the Abu Yousef al-Najjar hospital’s morgue. A neighbor’s 4-month-old girl was also killed.

Ahmed Omar rushed with other neighbors after the 1:30 a.m. strike to look for survivors, but said they only found bodies and body parts.

“It's a tragedy,” he said.

An Israeli airstrike later Saturday on a building in Rafah killed seven people, including six members of the Ashour family, according to the morgue.

Five people were killed in the Nuseirat refugee camp in central Gaza overnight when an Israeli strike hit a house, according to officials at the al-Aqsa Martyrs Hospital.

Elsewhere, Israeli forces shot and killed two Palestinian men at a checkpoint in the Israeli-occupied West Bank, the military said. It said the men had opened fire at troops stationed at Salem checkpoint near the city of Jenin.

Violence in the West Bank has flared since the war. The Ramallah-based Health Ministry says 491 Palestinians have been killed by Israeli fire.

Washington has been critical of Israeli policies in the West Bank. US Secretary of State Antony Blinken, who is expected in Israel on Tuesday, recently determined an army unit committed rights abuses there before the war in Gaza.

But Blinken said in an undated letter to US House Speaker Mike Johnson, obtained by the Associated Press on Friday, that he's postponing a decision on blocking aid to the unit to give Israel more time to right the wrongdoing. Blinken stressed that overall US military support for Israel’s defense wouldn't be affected.

The US has also been building a pier to deliver aid to Gaza through a new port. Israel's military confirmed Saturday that it would be operational by early May.

Hamas sparked the war by attacking southern Israel on Oct. 7, with militants killing around 1,200 people, mostly civilians, and taking around 250 hostage. Israel says the militants still hold around 100 hostages and the remains of more than 30 others.

Hamas on Saturday released a video showing hostages Keith Siegel and Omri Miran. It wasn't clear when the video was made. Both referred to the Jewish holiday of Passover, which began Monday. They called on Israel's government to reach a deal with Hamas. They almost certainly spoke under duress.

More than 34,000 Palestinians have been killed in Israel's offensive, according to the Health Ministry in Hamas-run Gaza, around two-thirds of them children and women. Its count doesn't distinguish between civilians and combatants. The ministry said 32 people killed were brought to local hospitals over the past 24 hours.

Israel blames Hamas for civilian casualties, accusing it of embedding in residential areas. Israel has reported at least 260 soldiers killed since the start of ground operations. (AP)