AMNA NAWAZ: Welcome to the "NewsHour."

A staggering milestone today in Gaza the Hamas-run Gaza Health Ministry says 10,000 Gazans, including 4,000 children, have been killed since the Hamas terrorist attack in Israel on October 7.

Israel says its ground operation has now cut off Gaza City in the north from the rest of the Gaza Strip.

GEOFF BENNETT: And Secretary of State Antony Blinken left the region today after rare public disagreements with America's closest Arab allies.

He described his efforts to secure a humanitarian pause and the release of hostages as a - - quote -- "work in progress."

Nick Schifrin starts our coverage with another day of funerals in Gaza.

Some of the images in this report are disturbing.

NICK SCHIFRIN: The body of a child, the body whose burden falls on four adult men.

Gazans say one month of war has spared no one.

The Hamas-controlled Ministry of Health number, 10,000, is unprecedented, even for a small strip of land that has suffered six words in 15 years.

The latest victims today, Israel said it was targeting a Hamas commander.

MOHAMMED, Gaza Strip Resident (through translator): It was night.

I was just sitting there when the bombing happened.

They pulled us out from under the rubble.

You can see the children, young boys and girls.

They were all martyred.

NICK SCHIFRIN: Israeli airstrikes continued today, including on a building inside the Al Shifa Hospital compound, among the victims, a desperate man trying to save a child.

Israel accuses Hamas of hiding in hospitals and released new footage today of tunnels next to and underneath Gaza in the north.

But Israel is increasingly focused on its ground operation, approaching closer to Gaza City.

Soldiers in Northern Gaza also captured what used to be a Scouts headquarters for kids, where they said Hamas launched rockets.

Israeli forces are trying to encircle Gaza City from three axes, the northeast into Beit Hanoun, the northwest along the Mediterranean Sea, and across Central Gaza, cutting the strip in two.

REAR ADM. DANIEL HAGARI, Spokesperson, Israeli Defense Forces (through translator): The forces on the ground are advancing according to the operational plan, moving forward, increasing the pressure deep in Gaza City.

NICK SCHIFRIN: But across the region, Israel's campaign is sparking widespread protest.

Today, it was in Ankara, Turkey, and included demonstrators with swastikas.

They followed Secretary of State Antony Blinken's meeting with Turkey's foreign minister and Blinken's attempts to convince the region the U.S. cares about Palestinians.

ANTONY BLINKEN, U.S. Secretary of State: We know the deep concern here for the terrible toll that Gaza is taking on Palestinians, on men, women and children in Gaza, innocent civilians, a concern that we share and that we're working on every single day.

We have engaged the Israelis on steps that they can take to minimize civilian casualties.

NICK SCHIFRIN: His Turkey visit capped a four-day regional tour... Good to see you.

BENJAMIN NETANYAHU, Israeli Prime Minister: Good to see you.

NICK SCHIFRIN: That began on Friday in Tel Aviv, where his requests to Prime Minister Benjamin Netanyahu for a pause... ANTONY BLINKEN: We see this as a way of further facilitating the ability to get assistance in.

NICK SCHIFRIN: ... were publicly rejected.

BENJAMIN NETANYAHU (through translator): Israel refuses any temporary cease-fire that does not include the return of our kidnapped hostages.

NICK SCHIFRIN: In Ramallah, Blinken discussed having the Palestinian Authority take over Gaza after the war.

But Palestinian Authority President Mahmoud Abbas called it impossible without a completed two-state solution.

And, in Amman, a rare public disagreement between the United States and two of its top allies in the region, Jordan and Egypt.

AYMAN SAFADI, Jordanian Foreign Minister (through translator): In the Arab countries, we demand an immediate cease-fire and end to this war and what results from it, killing innocent people, destruction, and we reject its description as a self-defense.

ANTONY BLINKEN: A cease-fire now would simply leave Hamas in place, able to regroup and repeat what it did on October 7.

MARWAN MUASHER, Former Jordanian Foreign Minister: The United States needs to understand that it is being seen in the region as complicit in the killing.

NICK SCHIFRIN: Marwan Muasher is Jordan's former foreign minister.

He acknowledges that Arab leaders' public anger does not match their private diplomatic messaging.

But he says the space between private diplomacy and public rage is shrinking.

MARWAN MUASHER: And so the call for a cease-fire is not just to please public opinion.

It is real.

And it stems out of the fact that, if a cease-fire is not effected soon, and if conditions of war allow Israel to transfer Palestinians into Egypt or into Jordan, that is a real concern for Jordan and Egypt.

NICK SCHIFRIN: Israel denies any plan to transfer population.

But, today, in the area of Southern Gaza that Israel promised would be safer, Gazans say the bombs do not stop and that nowhere feels safe.

For the "PBS NewsHour," I'm Nick Schifrin.