GEOFF BENNETT: Welcome to the "NewsHour."

More Americans are leaving Gaza as evacuations pick up speed following complicated negotiations.

Aid deliveries to the more than two million civilians in Gaza are still trickling in, but the need is far greater.

And, as Leila Molana-Allen reports, Israel is continuing its airstrikes and ground campaign in Northern Gaza.

LEILA MOLANA-ALLEN: Israel intensified its ground operation today, releasing this video it says shows troops operating deep inside Northern Gaza.

Israel Defense Forces Chief of Staff Herzi Halevi confirmed soldiers are now engaged in urban warfare.

LT. GEN. HERZI HALEVI, Chief of Staff, Israeli Defense Forces (through translator): IDF fighters have been operating in Gaza City for the past few days, encircling it from several directions, deepening the entrance of the IDF into Gaza and deepening our achievements.

LEILA MOLANA-ALLEN: As Israel advances... WOMAN: Mr. President, if you care about the Jewish people, as a rabbi, I need you to call for a cease-fire right now.

LEILA MOLANA-ALLEN: ... President Biden appeared last night to call for a -- quote -- "pause" in the fighting to facilitate aid deliveries after he was interrupted at an event.

National Security Council spokesperson John Kirby clarified today.

JOHN KIRBY, NSC Coordinator For Strategic Communications: What we're talking about are temporary, localized pauses in the fighting to meet a certain goal or goals, as I said, get aid in, get people out.

LEILA MOLANA-ALLEN: And before leaving again for the Middle East, Secretary of State Antony Blinken spoke to the enormous civilian death toll in Gaza.

ANTONY BLINKEN, U.S. Secretary of State: When I see a Palestinian child, a boy, a girl, pulled from the rubble of a collapsed building, that hits me in the gut as much as seeing a child in Israel or anywhere else.

So this is something that we have an obligation to respond to, and we will.

LEILA MOLANA-ALLEN: Gazans desperate to escape that fighting crowded the Rafah Border Crossing again today.

More foreign nationals were allowed to leave.

Suzan finally got out.

This was her fifth attempt.

But she left with mixed feelings.

SUZAN BESEISO, American Citizen in Gaza: Right now, I'm between ice and fire.

I don't know if I'm ever going to be able to see the family that I left behind or the friends that I left behind.

People are dying.

LEILA MOLANA-ALLEN: As people went out, aid trucks came in, also running low, fuel.

The Hamas-run Gaza Health Ministry says the main generator in Gaza's Indonesian Hospital failed today.

Israel claims Hamas is diverting fuel from the hospital.

Today, Israeli authorities released what they say is an intercepted phone call, where the hospital's manager talks about giving fuel to Hamas.

The "NewsHour" could not verify the authenticity of the recording.

Israel Defense Forces Chief of Staff Herzi Halevi expressed willingness to supply fuel to Gaza under strict supervision.

Prime Minister Benjamin Netanyahu said later that was not yet a commitment.

And as Gaza continues to be pounded by airstrikes, the army signaled today that it's ready to step up its attacks against Hamas, saying that Israel's air force is currently only using half of its aerial capability.

The IDF's bombardment already seems unrelenting on the ground.

Aerial footage showed massive destruction at the Al-Barij refugee camp after a strike on residential buildings today.

Meanwhile, residents in the Al-Maghazi refugee dug through this pile of debris that was once a home.

Abdal was with them.

ABDAL HADI MUSALLAM, Al-Maghazi Camp Resident (through translator): This house was bombed, including residents, civilians, children and the elderly, without any warning.

LEILA MOLANA-ALLEN: The fate of those civilians unknown.

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