GEOFF BENNETT: Welcome to the "NewsHour."

Israel's offensive in Gaza continues tonight, focused in the north, where fighting in Gaza remains around hospitals there.

Civilians, meantime, are caught between the Israel Defense Forces and Hamas' determination to hide among them.

AMNA NAWAZ: The government media office today in Gaza, run by Hamas, said today that the fighting has killed more than 13,000 civilians since the October 7 terror attacks by Hamas against Israel; 1,200 Israeli civilians were killed that day.

Nearly 240 hostages taken from Israel are being held by militants in Gaza.

Nick Schifrin reports.

NICK SCHIFRIN: Once again, a Gaza hospital is a battleground.

Tanks line the perimeter of the Indonesian Hospital in Northern Gaza.

Israel says Hamas gunmen were using the hospital as cover.

Inside, last week, injured children lined the hallways.

The WHO says as many as 700 people needed the hospital for treatment or shelter.

Today, the Hamas-controlled Gaza Ministry of Health denied its fighters use hospitals.

ASHRAF AL-QUDRA, Spokesperson, Palestinian Ministry of Health (through translator): The occupation has now put the Indonesian Hospital in the circle of death.

The hospital has been completely surrounded and sieged.

NICK SCHIFRIN: The hospital is in Northern Gaza, where Israel has asked all residents to leave, and where American researchers found Israel's air campaign, has damaged or destroyed roughly 50 percent of all housing units.

Now Israeli officials are urging Gazans to flee to an even smaller location in the south, Al-Mawasi, roughly the size of Los Angeles' LAX Airport.

Israel continues to launch airstrikes in the south, ahead of an expected ground invasion, that yesterday Deputy National Security Adviser Jon Finer said needed to be well-planned.

JON FINER, U.S.

Principal Deputy National Security Adviser: We think that their operations should not go forward until those people, those additional civilians have been accounted for in their military planning.

NICK SCHIFRIN: The U.S. has also been pushing for more aid to arrive into Southern Gaza.

Today, a Jordanian field hospital passed through the Rafah Crossing.

This weekend, the most significant delivery of fuel also crossed the border.

Desperate for assistance, Gazans welcomed the help and appealed for more.

MOHAMAD ZOROUB, Gaza Strip Resident (through translator): We are so thankful.

I hope all Arabs come together and stand with us, like the people of Jordan did today.

And I beg for all Arabs to unite, stand with us, and help us to end the siege and the war here.

NICK SCHIFRIN: But Israel vows to pursue its siege until Hamas is destroyed, even underneath Gaza's largest hospital.

Yesterday, the Israeli military released this video showing what it called a Hamas tunnel, with its own electricity and ventilation, and protected by a blast-proof door and photos of Hamas fighters on October 7, holding hostages kidnapped from Israel walking through Shifa's hallways.

But when Israel raided the hospital, there were still patients inside, including the most vulnerable.

Today, those premature babies arrived in Egypt, the blameless caught in the crossfire loaded one by one into mobile incubators.

Lobna Al-Saik had to choose between evacuating with her youngest daughter or staying with her older children.

LOBNA AL-SAIK, Mother of Premature Baby (through translator): They are innocent children, premature babies, not to mention toddlers, 3 years old or 5 years old.

I left my three children in Gaza.

I didn't even get a chance to hug them, because I couldn't leave my daughter in this state.

JOHN KIRBY, NSC Coordinator For Strategic Communications: Especially, we want to see the children and women get released.

NICK SCHIFRIN: The most vulnerable Hamas hostages are the focus of ongoing intense diplomacy between the U.S., Qatar and Israel.

Hamas would release dozens of hostages kidnapped on October the 7th in exchange for increased humanitarian aid and the release of Palestinians held in Israeli detention.

Today, the Israeli government held a tense meeting with hostage family members.

Other families met with the Israeli war cabinet.

Meirav Leshem Gonen's daughter was kidnapped from the music festival.

MEIRAV LESHEM GONEN, Mother of Hostage: Any move they are doing will not take any responsibility from them to return all the hostages back alive here to us, to our arms.

It's my Romi.

It's Shai Wenkert's son... MAN: Son Omer.

MEIRAV LESHEM GONEN: ... and all the other hostages.

NICK SCHIFRIN: It's just one part of a traumatized Israeli society that today continues to bury its dead; 388 soldiers have died since October the 7th, the most in 20 years.

For the "PBS NewsHour," I'm Nick Schifrin.