GEOFF BENNETT: Welcome to the "NewsHour."

A Hamas delegation left Cairo this evening and is expected to return with a response to the latest cease-fire proposal.

That's as fraught negotiations continue nearly seven months into the war in Gaza.

AMNA NAWAZ: Secretary of State Blinken is back in the region today, and he pressed not just for a cease-fire and for hostage release, but for much more humanitarian aid into Gaza.

Meantime, the Israeli bombardment continues in Gaza's south, with the city of Rafah in their sights.

Homes in Southern Gaza today nothing more than crushed concrete and twisted bodies, amid this wreckage, one small survivor, just 2 months old.

UMM FAYEZ ABU TAHA, Rafah, Gaza, Resident (through translator): We took her from under the rubble, thank God.

Was she holding a rocket or was she standing near tanks?

What's her fault?

AMNA NAWAZ: Palestinian medics say at least 22 people were killed in Israeli airstrikes on Rafah last night.

As the barrage continues, pressure mounts for Hamas and Israeli leaders to stop the violence.

The International Criminal Court has been investigating possible Israeli war crimes in Gaza.

Recent reports cite Israeli officials as worried that arrest warrants may be imminent.

On Friday, Prime Minister Benjamin Netanyahu responded, saying -- quote -- "The threat to seize the soldiers and officials of the Middle East's only democracy and the world's only Jewish state is outrageous."

Hamas leaders could also face warrants for the horrific October 7 attacks.

Neither Israel nor the U.S. recognizes the ICC, but other countries could arrest anyone with an outstanding warrant.

The State Department today said any ruling from the ICC would not apply.

VEDANT PATEL, Principal Deputy State Department Spokesperson: On this investigation, our position is clear.

We continue to believe that the ICC does not have jurisdiction over the Palestinian situation.

AMNA NAWAZ: Meanwhile, thousands of Israelis rallied in Tel Aviv calling for a hostage release and cease-fire deal ahead of negotiators from Israel and Hamas arriving in Cairo today.

The White House said President Biden would call leaders from Qatar and Egypt today.

Hamas has released multiple videos of hostages in the last week, including Illan Siegel's American father, Keith.

ILLAN SIEGEL (Daughter of Hamas Hostage): Seeing my father today only emphasizes to all of us how much we must reach a deal as soon as possible and bring everyone home.

AMNA NAWAZ: Secretary of State Antony Blinken returned to the Middle East today for his seventh trip since the war began.

At the World Economic Forum in Saudi Arabia, he called on Hamas to act.

ANTONY BLINKEN, U.S. Secretary of State: Hamas has before it a proposal that is extraordinarily, extraordinarily generous on the part of Israel.

And in this moment, the only thing standing between the people of Gaza and a cease-fire is Hamas.

AMNA NAWAZ: At the same forum, regional leaders stressed that peace would only follow a two-state solution.

Saudi Foreign Minister Faisal Bin Farhan: PRINCE FAISAL BIN FARHAN AL SAUD, Saudi Foreign Minister: In order for us to be able to talk about a sustainable pathway to stability, to security, including for Israel, we're going to have to talk about a Palestinian situation where the Palestinians have hope.

AMNA NAWAZ: At a meeting of the Gulf Cooperation Council, Blinken pledged to carry that message to Israel.

ANTONY BLINKEN: The most effective way to address the humanitarian crisis in Gaza, to alleviate the suffering of children, women, and men, and to create space for a more just and durable solution is to get a cease-fire and hostages home.

But we're also not waiting on the cease-fire to take the necessary steps to meet the needs of civilians in Gaza.

AMNA NAWAZ: Palestinians in Gaza find pockets of peace wherever they can.

For some sheltering in Deir al Balah, that means a brief family respite at the beach, hoping the waves will drown out the sound of drones overheard.

Umm Malik Abd Rabbo brought her kids here today.

UMM MALIK ABD RABBO, Displaced Gazan (through translator): Every time there's a plane in the sky, it frightens the kids here.

Although I came here to give the children some semblance of safety, fear is fear.

Children get scared.

AMNA NAWAZ: Her husband, little Mayar's father, is still in Northern Gaza.

MAYAR ABD RABOO, Displaced Gazan (through translator): I came to the beach because I haven't been here in seven months.

I came to have fun with my cousins, and my sister and my brothers.

I don't feel safe and I hope the war ends so I can go back to my dad.

AMNA NAWAZ: For now, there is safety on this sand.

But just miles away in Rafah, the war rages on.

The State Department announced today that five units of the Israeli military were found to have violated human rights in incidents before the current war, and not in Gaza.

The U.S. says those violations are being addressed, and will not affect U.S. weapon sales to Israel.