GEOFF BENNETT: Welcome to the "NewsHour."

A new phase in the bloody war in Gaza is now under way.

Israel is assaulting the largest city in the south, Khan Yunis.

Most of Gaza's population is now in that region.

AMNA NAWAZ: The war is now nearly two months old, with a death toll fast approaching 20,000, mostly Palestinian.

Despite pleas for more precision and fewer civilian killings from the U.S. and other Israeli partners, the thunderous campaign to root out Hamas in Gaza continues.

After weeks of fighting Hamas in Gaza's north and a weeklong pause inviting, a new phase in the war, as the IDF enters Gaza's second largest city.

LT. GEN. HERZI HALEVI, Chief of Staff, Israeli Defense Forces (through translator): Those who thought that the IDF would not know how to renew the fighting after the pause inviting were mistaken.

And Hamas is already feeling this.

AMNA NAWAZ: Israel believes that Yahya Sinwar, Hamas' leader in Gaza, is hiding among civilians there.

IDF commanders on the ground said this fight is their campaign's fiercest so far, as they aim to wipe out Hamas.

According to the U.N., Israel's bombardment has so far destroyed more than 46,000 housing units in Gaza and displaced an estimated 1.87 million people, or about 80 percent of the entire population.

And for the first time, Israeli officials released their own death toll estimates in Gaza, saying 15,000 Palestinians have been killed, about 30 percent of whom Israel claims were militants.

Gaza's Hamas run-Health Ministry says about 16,300 Palestinians have been killed, 70 percent of whom they say were women and children.

In Israel today, families of hostages still held by Hamas met with Prime Minister Benjamin Netanyahu and said time is running out.

RUBY CHEN, Father of Hamas Hostage: Each day that passes by, they are dying slowly each day.

We need to get them out immediately, whatever the price might be.

AMNA NAWAZ: They were reportedly told by Netanyahu in that meeting that there is -- quote -- "no possibility right now to bring everyone home."

Some families reportedly walked out in response.

And in the Israeli Knesset, a passionate appeal from Shir Siegel, whose mother, Aviva, was released from captivity in Gaza, but her father, Keith, still remains.

SHIR SIEGEL, Daughter of Hamas Hostages: While we speak, there's a Holocaust a three-hour drive from here.

Why is it more important for Bibi to kill Hamas leaders and not to bring my father back home?

AMNA NAWAZ: In an evening speech, Netanyahu responded.

BENJAMIN NETANYAHU, Israeli Prime Minister (through translator): Cabinet members and I met today with families of the hostages, those who we have already returned home and those who we are doing everything we can to get back.

AMNA NAWAZ: A Hamas representative said today they will not release more hostages until Israel's offensive in Gaza stops.

OSAMA HAMDAN, Hamas Spokesperson (through translator): We assure here again that there will be no negotiations or exchange of hostages until the aggression against our people and the steadfast Gaza Strip stops.

AMNA NAWAZ: Gazan civilians just want the horrors of war to end.

At Khan Yunis's Nasser Hospital today, victims lined the emergency room floor after another night of Israeli airstrikes, leaving some speechless.

MAN (through translator): There was shelling.

I can't even talk about it.

AMNA NAWAZ: Um Ibrahim's entire immediate family was left crushed under a building.

UM IBRAHIM AL NAJJAR, Gaza Strip Resident (through translator): Where are the ambulances?

I lost my children and my husband.

Where is the United Nations?

My children, my children, since 10:00 p.m., are still under the rubble.

AMNA NAWAZ: Residents of Khan Yunis, once declared safe by Israel, are now trying to escape to the southern town of Rafah on the Egyptian border.

Awaiting them there, a swelling humanitarian disaster, a line of hundreds at the only working water station in the city.

Ahmad Al-Attar has to walk more than a mile every day to fill up.

AHMAD AL-ATTAR, Displaced Palestinian (through translator): You have to wait for three hours in line.

You hold water on your shoulders.

The situation is very hard.

We take a bath once a month.

I am 63 years old and I'm carrying the gallon my shoulder for more than a mile.

AMNA NAWAZ: Others are packed into tent cities with no idea where they will go next.

Meanwhile, after a surge of settler violence against Palestinians in the West Bank since the war began, the U.S. State Department, in a rare move, imposed travel bans on dozens of Israeli settlers.

State Department spokesperson Matthew Miller: MATTHEW MILLER, State Department Spokesman: These acts threaten West Bank stability in the immediate term and take us further away from a future in which Palestinians and Israelis can both live in -- both can live in peace and security in two states.