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 months-long war and stave off a possible Israeli ground offensive into the southern Gaza city of Rafah.

Senior Hamas official Khalil al-Hayya said the Palestinian militant group was evaluating Israel’s proposal, and “upon completion of its study, it will submit its response.”

He gave no details of Israel's offer but said it was in response to a proposal from Hamas 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.

Hamas’ statement came hours after a high-level Egyptian delegation wrapped up 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.

It was not immediately clear whether Israel’s latest response to Hamas on a cease-fire was directly related to Friday’s visit to Tel Aviv by Egyptian mediators.

The discussions between Egyptian and Israeli officials focused on the first stage of a multi-phase 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.

The 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 larger deal to end the war, the official said.

As the war drags on and casualties mount, there has been growing international pressure for Hamas and Israel to reach an agreement on a cease-fire and avert a possible Israeli attack on Rafah, where more than half of Gaza’s 2.3 million people have sought refuge after fleeing fighting elsewhere in the territory.

Israel has been insisting for months it plans a ground offensive into Rafah, on the border with Egypt, where it says many remaining Hamas militants are holed up, despite calls for restraint from the international community including Israel’s staunchest ally, the United States.

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

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

Early Saturday, an Israeli airstrike hit a house in Rafah’s Tel Sultan neighborhood, killing six people, including four children, according to officials at a local hospital.

The strike killed a man, his wife and their three sons, aged 12, 10 and 8, according to records of the Abu Yousef al-Najjar hospital’s morgue. A neighbor’s four-month-old girl was also killed, the records showed.

Elsewhere, Israeli forces shot and killed two Palestinian men in an exchange of fire at a checkpoint in the Israeli-occupied West Bank, the military said.

Violence in the West Bank has flared since the war started. Since then, 491 Palestinians have been killed by Israeli fire in the territory according to the Ramallah-based Health Ministry,

The Israeli army said the two men were killed after they opened fire from a vehicle at Israeli troops stationed at Salem checkpoint near the Palestinian city of Jenin.