AMNA NAWAZ: Turning to our other top story, the war in Gaza between Israel and Hamas, the Israel Defense Forces' ground operation is engaged in heavy fighting focused on the north, and Israel's punishing bombardment of Gaza continues.

America's top diplomat laid out the most specific plan to date that the U.S. wants for postwar Gaza.

Leila Molana-Allen is in Tel Aviv again tonight.

LEILA MOLANA-ALLEN: In the Northern Gaza Strip, Israel's ground invasion grinds on.

IDF spokesman Daniel Hagari said today troops have gained ground.

REAR ADM. DANIEL HAGARI, Spokesperson, Israeli Defense Forces (through translator): Hamas has lost control and is continuing to lose control in the north.

LEILA MOLANA-ALLEN: The IDF also claims they have made progress demolishing Hamas' network of underground tunnels and have killed hundreds of Hamas militants, including a leading weapons-maker today.

In Tokyo, group of seven diplomats weighed in on the war, including Secretary of State Antony Blinken.

ANTONY BLINKEN, U.S. Secretary of State: The G7 ministers reaffirmed our staunch support for Israel's right and obligation to defend itself.

LEILA MOLANA-ALLEN: They issued a unified statement after two days of intense talks.

It backs Israel's retaliation against Hamas while calling for urgent action to help civilians in Gaza.

ANTONY BLINKEN: We all agreed that humanitarian pauses would advance key objectives, to protect Palestinian civilians, to increase the sustained flow of humanitarian assistance, to allow our citizens and foreign nationals to exit, and to facilitate the release of hostages.

LEILA MOLANA-ALLEN: And on Gaza after the war, Secretary Blinken made clear there's no room for Hamas.

ANTONY BLINKEN: Gaza cannot be -- continued to be run by Hamas.

It's also clear that Israel cannot occupy Gaza.

LEILA MOLANA-ALLEN: He did warn of a -- quote -- "transition period" afterward, but reaffirmed that Palestinians ultimately need to govern the enclave.

Prime Minister Benjamin Netanyahu said he foresees Israel maintaining security control over Gaza indefinitely, although other Israeli officials later clarified that they don't intend to occupy Gaza after the war.

And, as the IDF gains ground inside Gaza City, it reports that 32 of its soldiers have now been killed since the ground invasion began.

Across the border, IDF soldiers rotating out of the battle zone wait at rest stops like these across Southwestern Israel, which has become a staging ground for the war.

Many of them are run by volunteers.

Kobi and his family started this donations tent on their own dime.

Within days, the entire community was pitching in.

Now they're feeding 1,000 soldiers a day.

KOBI GANON, Israeli Volunteer: They seem the zombies, like they came back from hell.

Sometimes, they come from the area and they say, do you have soap?

I cannot smell myself, because it was all -- from all the bodies.

LEILA MOLANA-ALLEN: Kobi says Israelis living here are of one mind about the goals of this war.

KOBI GANON: Everyone coming here, they have a mission to save their own kids, to save their own family, whether they were in the killing area, or even if they're not, because they know they're coming next.

I'm here because I know, if I'm not here supporting our soldiers, my kids will be next.

LEILA MOLANA-ALLEN: Back in Gaza, Palestinians packed the roads by foot, car and horse car, fleeing the fighting in the north for yet another long day.

"NewsHour" producer Shams Odeh was there.

SHAMS ODEH: We are now in the main street of Gaza City, Salah al-Din street.

It's the main street from Gaza, north of Gaza to the south of Gaza.

People are crossing since the morning.

Thousands of them left Gaza, crossing the streets to the south, looking for the safety.

LEILA MOLANA-ALLEN: More than 70 percent of Gaza's 2.3 million residents have left their homes, including Zayed.

ZAYED KHADER, Gaza Strip Resident (through translator): We saw everyone evacuating, so we evacuated.

They said go to the Nuseirat refugee camp.

And here we are, walking, no food, no water, no money.

LEILA MOLANA-ALLEN: Waiting for them in the south, more devastation.

Nuseirat refugee camp in the area Zayed and so many others were told to flee to was hit by an Israeli airstrike today.

At least 18 people were killed, but others believe the death toll is higher.

Gasping for air between the sobs, Anas says dozens were killed in his uncle's house.

ANAS SHEHADA, Gaza Strip Resident (through translator): They bombed our house and my uncle's house.

There's maybe 30 people in there now.

Under the rubble could be about 30 to 40 people.

Accept them as martyrs, please, lord.

LEILA MOLANA-ALLEN: Others in Southern Gaza are living packed into tent cities.

Many of their homes have been destroyed.

They have no idea where they will go next.

For the "PBS NewsHour," I'm Leila Molana-Allen in Tel Aviv.