AMNA NAWAZ: Welcome to the "NewsHour."

We are entering the fourth week of war between Israel and Hamas in Gaza, as Israel's air campaign continues and the death toll mounts.

GEOFF BENNETT: Israel is now fighting Hamas on the ground in Gaza, with troops moving methodically in the northern end of the strip, while, in the south, more than a million Gazans await aid.

Leila Molana-Allen again starts our coverage.

LEILA MOLANA-ALLEN: For the fourth day straight, tanks and armored vehicles rolled into Gaza as part of Israel's growing ground offensive.

At his first press conference since the October 7 terror attacks, Prime Minister Benjamin Netanyahu reiterated that Israel will not consider a cease-fire.

BENJAMIN NETANYAHU, Israeli Prime Minister: Calls for a cease-fire are calls for Israel to surrender to Hamas, to surrender to terrorism, to surrender to barbarism.

That will not happen.

LEILA MOLANA-ALLEN: And Israel's longest-serving premier said he will not resign, despite growing anger at his government among Israelis.

BENJAMIN NETANYAHU: The only thing I intend to have resign is Hamas.

We're going to resign them to the dustbin of history.

That's my goal.

LEILA MOLANA-ALLEN: A goal apparent over Gaza City today, its skyline still filled with explosions, including in areas near the city's largest hospitals.

The Palestinian Red Crescent yesterday released video from inside al-Quds Hospital after a nearby Israeli rocket attack.

Areas near Al Shifa Hospital have also been hit in recent Israeli airstrikes.

Israel says Hamas hides one of its main military command centers beneath the hospital.

But Al Shifa is also home to 50,000 displaced Palestinians.

Nearby streets are becoming tent cities, with their own food and clothes stalls.

MOHAMMED MAAROUF, Displaced Palestinian (through translator): Now the Israelis say that they will hit Al Shifa.

The threats do not frighten us.

Let them launch airstrikes as much as they want.

We are all martyrs in the end.

LEILA MOLANA-ALLEN: The conflict has already exacted an excruciating toll on civilians, with thousands dead, even the most vulnerable.

So far, more than 3,000 children have been killed, according to Save the Children.

That's more than the total number of children killed annually in conflict zones since 2019.

South of the city, Israeli tanks today temporarily blocked Salah al-Din, Gaza's main north-south highway.

A local journalist recorded this video as a tank appeared to open fire on a civilian car, killing three people.

Palestinian residents say the route was blocked for over an hour, complicating Gazans' already-fraught efforts to move south.

"NewsHour" producer Shams Odeh was there.

SHAMS ODEH: The Israelis asked all the people a few days ago to leave Gaza to the south.

Now the Israeli army cut the way at all between the north and the south.

Any car crossing now to Gaza, they attack and target the car.

LEILA MOLANA-ALLEN: But Gazans who escaped to the south from Israel's military campaign in the north found no protection there.

This school in the town of Al-Mughraqa used to be a safe haven, now shattered after a nearby bombing, the youngest ones left with whatever they could carry, as crowds crammed into one truck preparing to flee without anywhere to go.

MAN (through translator): There are almost 2,000 of us here.

We've been here for two days with missiles thrown over our heads.

We are evacuating again.

We don't know where to go.

LEILA MOLANA-ALLEN: In Israel, artillery positions and military encampments roll out along the Gaza border.

The IDF has confirmed its troops are now on the ground fighting inside Gaza.

We can hear small-arms fire, the sound of constant airstrikes landing, behind me, smoke rising from towns in the northern part of the strip, as the air force continues its unrelenting bombardment.

Today, Israel said it killed four members of Hamas, and Israeli forces are expanding their military campaign, gradually building up forces to eliminate pockets of resistance and destroy enemy infrastructure.

This soldier is part of an IDF team that has been searching the border area for Hamas explosives and booby-traps to clear the way as ground forces move in.

As the operation expands, their task will only get more complicated.

MAN: I think one of the biggest threats is explosive ordnance set there to harm our teams moving forward.

So that could be in open terrain.

It could be in built terrain.

It could be underground terrain.

LEILA MOLANA-ALLEN: Three weeks later, bomb squads are also still working on safely detonating and removing thousands of potentially live explosives left over after the brutal Hamas attacks on farming villages and at a music festival, where nearly 300 young people were killed and dozens kidnapped.

MAN: We found an enormous amount of explosives, ordnance.

LEILA MOLANA-ALLEN: Meirav Leshem-Gonen's 23-year-old daughter, Romi, was at that party.

As rockets began to rain in from Gaza that morning, Romi stayed on the phone with her mom for hours, desperately trying to escape the terrorists who had invaded the festival site.

The friend trying to drive them home was killed.

Then her best friend was shot dead next to her.

MEIRAV LESHEM-GONEN, Family Member of Hostage: At 10:14, I got the most horrifying phone call I could get.

She was calling me and crying, saying: "Mommy, I was shot.

I'm bleeding.

I'm afraid I'm going to die."

LEILA MOLANA-ALLEN: Since October 7, they have heard nothing.

But Meirav and her four other kids are working night and day to find Romi and bring her home.

Like many families of the hostages, she's angry and terrified that the government and army have launched a war on Gaza by land and air while their loved ones are still trapped inside.

MEIRAV LESHEM-GONEN: It's frightening just to think they're widening the maneuver, and my daughter is there, not just my daughter, other people, babies, small kids.

LEILA MOLANA-ALLEN: One hostage was freed today during the ground invasion.

Israeli soldier Ori Megidish has been reunited with her family.

More releases are expected as the ground mission continues.

Meanwhile, Israeli security forces are cracking down throughout the West Bank.

The Israel Defense Forces released video of an overnight raid in the northern city of Jenin.

Four Palestinians were killed and many more injured.

And violence against Israelis is also spreading.

In East Jerusalem, Israeli police said an officer was stabbed by a Palestinian.

And even far from the front lines, in the Dagestan region of Russia, a mob stormed an airport after a flight from Israel landed in the mostly Muslim region on Sunday.

Hundreds pushed their way into the airport searching for Jews, in a sinister echo of pogroms past.

And harassment and violence are increasing against both Jews and Muslims everywhere as the world watches this escalating war, Geoff.

GEOFF BENNETT: Leila, I know that you have spent the past few days reporting along the border with Gaza ever since the intensified ground raids started.

What more can you tell us about how they're playing out?

LEILA MOLANA-ALLEN: I have ever since Friday night, when they announced that they were increasing their ground operation in Gaza.

Now, of course, what's happening from the air, we can all see, these unrelenting airstrikes on Gaza, smoke constantly rising.

I have been down on that border, the sound every half-minute of something being sent there, either artillery fire or an airstrike, and then, of course, smoke rising from the buildings in front of us.

Now, in terms of what's happening with the ground forces that have gone in, it was very difficult to get information at the beginning.

We are now hearing more.

It does seem that, at the beginning of the weekend, they were focusing on this northeastern corner of Gaza, trying to move through there, trying to get past the border fence.

We know there were fights, hand-to-hand fights there with Hamas terrorists on that border fence.

And by today, they have now reached Gaza City on the ground there.

We know that they blocked the top of that vital artery through Gaza today for a while.

Now, I was speaking to a couple of soldiers that had just come back over the border from fighting in Gaza this weekend.

What they were saying is, they're incredibly worried about two things, firstly, of course, these tunnels, hundreds of miles of tunnels underneath Gaza that Hamas are using.

And, secondly, when they come out, often from behind the tank and attack, they then move into this densely packed environment in Gaza, one of the most densely packed environments in the world.

And it's then urban warfare.

So they're facing multiple threats.

They have had their first few casualties yesterday and today.

GEOFF BENNETT: And as we saw in your report, Leila, the prime minister held a press conference today.

He was asked if he would step down by a reporter.

He refused to do so.

Give us a sense, though, of the public opinion and how that might affect his political standing.

LEILA MOLANA-ALLEN: Well, there are three issues here.

Of course, the first is people in the country so incredibly angry that Mr. Security, as Netanyahu was known, could have allowed this to happen in the first place, this massive intelligence failure.

Secondly, at the end of last year with this election, Netanyahu made a deal with some very right-wing elements to form a government, and many people feel that that split in society, those divisions are what distracted the security forces of the government from this threat that was coming.

And thirdly now, families of these hostages absolutely furious with him that these ground raids are happening, these huge air assaults happening while their families are still inside Gaza.

Now, he has apologized about the intelligence failure, but he said that he is going to go forward with this war.

And we all suspect that he hopes that, if he wins this war, all that will be forgotten and he will be the hero of Israel again.

GEOFF BENNETT: Leila Molana-Allen, reporting tonight in Tel Aviv.

Leila, thank you.