GEOFF BENNETT: Welcome to the "NewsHour."

Today marks one month since the Hamas terror attacks of October 7.

In Israel, there were vigils of remembrance.

And, in Gaza, the fighting and killing continues.

Late today, President Biden said he had asked Israeli Prime Minister Netanyahu for a pause in fighting.

AMNA NAWAZ: The Israeli army has now encircled Gaza City in its pursuit of Hamas, as tens of thousands of terrified civilians stream toward Southern Gaza, a fraught and dangerous path amid ongoing Israeli bombardment.

Once again this evening, Leila Molana-Allen begins our coverage.

LEILA MOLANA-ALLEN: Along the southbound road of the Gaza Strip, Palestinians flee from the north in droves, some waving white flags, many of them children, making the long walk without shoes.

In the distance, smoke rises over the city Naseem left behind, his home under siege.

NASEEM AL-DADA, Displaced Gazan (through translator): We are heading south, as they told us to do.

We are walking and don't know to don't know where we will go.

To schools, to sleep on the streets, to sleep at people's places?

Only God knows.

LEILA MOLANA-ALLEN: The exodus in Gaza follows new evacuation orders from Israel.

Ground forces have surrounded Gaza City.

And the military claims it has already destroyed Hamas strongholds, including those hidden underground.

MAJ. GEN. YARON FINKELMAN, Israeli Defense Forces (through translator): For the first time in decades, the Israeli Defense Forces are fighting in the heart of Gaza City, at the heart of terrorism.

This is a complex and difficult war.

And, to my sorrow, it also comes at a price.

LEILA MOLANA-ALLEN: For many, leaving the city center isn't an option.

Gaza's largest hospital, Al Shifa, has looked like this for the past month, crammed inside and out with thousands of civilians, some of them patients, others homeless.

Lama now has nowhere else to sleep but on the floors of these hallways.

LAMA, Displaced Gazan (through translator): Look at our situation.

Is this a life that we are living?

We have no food, no electricity or water.

We sleep in the corridors, without any blankets.

My daughter died last Friday at Al Shifa.

My daughter died a martyr, and I remain a patient.

LEILA MOLANA-ALLEN: Today, U.S. officials said more than 400 American citizens have now been safely evacuated from the strip.

And the State Department said the U.S. will not support any forced relocation of Palestinians outside of Gaza.

One month on, Israelis commemorated the victims of the October 7 Hamas terror attacks and prayed for those still held hostage in Gaza in candlelit vigils across the country.

Earlier today, crowds gathered for a moment of silence.

BENJAMIN NETANYAHU, Israeli Prime Minister: As far as tactical little pauses, an hour here, an hour there.

LEILA MOLANA-ALLEN: In an ABC interview last night, Israel's Prime Minister Benjamin Netanyahu maintained his opposition to a cease-fire and hinted at his intentions for the Gaza Strip in the long term.

BENJAMIN NETANYAHU: I think Israel will - - for an indefinite period will have the overall security responsibility, because we have seen what happens when we don't have it.

When we don't have that security responsibility, what we have is the eruption of Hamas terror on a scale that we couldn't imagine.

LEILA MOLANA-ALLEN: But back in Gaza, what happens after the war, who wins, who loses, who governs whom, is the last thing on people's minds.

Most urgent here is survival.

This neighborhood in Khan Yunis was jolted awake by a nighttime airstrike.

Abu Jihad says the chances of narrowly dodging strike after strike are growing slimmer by the day.

ABU JIHAD, Gaza Resident (through translator): Thank God we are safe, but I swear we are waiting for death in each moment.

It's a suspended death.

LEILA MOLANA-ALLEN: One brutal month of war gone by, but no hope for an end in sight.

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