GEOFF BENNETT: Hamas formally responded to an Israeli-backed cease-fire proposal, but did not fully approve it, mediators announced today.

AMNA NAWAZ: Hamas' reply comes 11 days after President Biden revealed the three-phase cease-fire proposal that would begin with a temporary cease-fire.

Nick Schifrin is here now.

He's been following all of this.

So, Nick, what do we know about Hamas' reply?

NICK SCHIFRIN: A regional official, Amna, tonight tells me that Hamas' reply was -- quote -- "positive."

And Hamas and the militant group, Palestinian Islamic Jihad have released a statement tonight saying -- quote -- "The Palestinian delegation voiced willingness to deal positively in order to reach an agreement."

But it also described the -- quote -- "necessity of completely stopping the ongoing aggression against Gaza and the withdrawal of Israeli forces from the entire Gaza Strip."

And that suggests that Hamas' demanding the text matches what they are demanding in public, a permanent guaranteed cease-fire.

The deal only requires Israel to commit to a temporary cease-fire that would continue as long as the two sides are negotiating.

So, as John Kirby, the National Security Council spokesman, said today, it is positive that Hamas has formally responded.

It's not clear that it's enough to bridge the two sides' gap.

GEOFF BENNETT: And, Nick, what has Israel said in response?

NICK SCHIFRIN: Well, today, Secretary of State Antony Blinken said that Prime Minister Benjamin Netanyahu committed to this deal.

It is, of course, an Israeli-backed deal.

But Netanyahu continues in public to vow to destroy Hamas militarily.

U.S. officials remain concerned, Geoff, that both sides are more interested in blaming the other for the failure of these talks than they are for actually making progress.

But U.S. mediation will continue, U.S. diplomatic pressure will continue, because, frankly, U.S. officials think this is really the only way to end the war that has devastated so much of Gaza.

Today, the U.S. committed another $404 million in humanitarian assistance, despite so many limitations on aid delivery that have left Gazans largely on their own.

Her stage is Gaza's ruins, and her audience is Gaza's displaced children.

RAHAF NASSER, Medical Student: I lost all my memories, all my childhood toys in my home, so I borrowed my father's friend's guitar to continue to deliver my message to the world.

NICK SCHIFRIN: Before the war, 19-year-old Rahaf Nasser was studying medicine.

Now she tries to heal with music.

RAHAF NASSER: Our children love to live, love to be alive, to play with each other.

Here, we cannot do anything of that.

They cannot do anything of that.

They just want peace.

ANTONY BLINKEN, U.S. Secretary of State: There is no time to waste, given the hell that hundreds of thousands of Palestinians are enduring every single day.

NICK SCHIFRIN: Today, Secretary of State Antony Blinken addressed a conference designed to surge aid to Gaza.

Martin Griffiths is the U.N.'s humanitarian coordinator.

MARTIN GRIFFITHS, U.N. Undersecretary-General for Humanitarian Affairs and Emergency Relief Coordinator: There was a unanimous horror at the vast toll of death, injury, destruction, displacement, serial displacement, trauma and deprivation suffered by the people of Gaza in just nine months.

NICK SCHIFRIN: And the most vulnerable are Gaza's youngest.

At this makeshift school in Central Gaza, they learn to live.

But, in Southern Gaza, UNICEF says nearly 3,000 are at risk of dying, and across Gaza, 90 percent lack enough food.

Israel has opened the southern crossing Kerem Shalom, and hundreds of Israeli-sponsored trucks are entering.

But U.S. and Israeli officials say distribution inside Gaza is limited because there aren't enough trucks, and the Rafah Crossing remains closed, with aid trucks backed up in Egypt.

And so, at already overwhelmed hospitals, there's a shortage of generators and fuel to provide power and supplies to save the city.

And to discuss the medical crisis, as well as the overall humanitarian situation in Gaza, I'm joined by Avril Benoit, chief executive officer of Doctors Without Borders USA.

Avril Benoit, thank you very much.

Welcome back to the "NewsHour."

After this past Saturday's rescue of four Israeli hostages that Hamas says killed more than 270 people, about 700 patients arrived in the Al-Aqsa Hospital, where you have staff.

Your team was working there.

Who did they treat and what were their injuries?

AVRIL BENOIT, Executive Director, Doctors Without Borders USA: The injuries were horrific.

At Al-Aqsa Hospital, yes, there were 420 severely wounded that came in, dismemberments, severe trauma.

You had a lot of open fractures, shrapnel wounds, as you would expect, a lot of burn injuries, a lot arriving who were already dead wrapped in blankets, in plastic, 190 in that one day alone were brought to the hospital and confirmed as dead on arrival.

NICK SCHIFRIN: You have some 400 Palestinian and expat doctors, nurses and staff in Gaza.

Are they able, at this point, to deliver the health care that they want?

AVRIL BENOIT: No, certainly not.

And there isn't a humanitarian who will tell you that anything is near being acceptable.

And when we think back to the orders from the International Court of Justice back in January imploring and insisting that Israel make sure that humanitarian aid could reach people in order to prevent conditions of genocide, we have not really seen an improvement and, at various times such as since the beginning of June, a deterioration.

Unfortunately also is that these mass casualty influxes where you have got hundreds of people coming into a hospital, even a well-equipped major hospital in the United States that's properly staffed, has all that it needs, has electricity, clean water for cleaning up and so on, even they would struggle with the number of patients.

NICK SCHIFRIN: Hundreds of trucks are getting in to Southern Gaza via Kerem Shalom, as well as into Northern Gaza, half of which are facilitated by Israel itself.

And what U.S. officials and Israeli officials I talked to say is that the big problem is the lack of trucks that can actually distribute all of that aid inside of Gaza.

Is that something that you are specifically seeing, that some of this aid is arriving to the edge of Gaza, but not able to be distributed inside?

AVRIL BENOIT: Without a doubt.

You have got the shortage of fuel, which is a serious impediment for even the truck drivers that are willing to take the risks of going through so many volatile checkpoints, where anything can happen.

Sometimes, the violence is unpredictable.

And where there is a lack of respect for the delivery of humanitarian aid, the indiscriminate violence, the targeted violence against humanitarians, it's -- it makes for really difficult conditions, and it doesn't help to be blamed then by the Israeli propaganda saying, well, look, the humanitarians already been doing their job.

Well, ultimately, all the belligerents are responsible for creating conditions that would allow humanitarian aid to come in, in accordance with humanitarian law.

And that's just not what we're seeing.

NICK SCHIFRIN: When you refer to belligerents, are you speaking about the Israelis, Hamas, or both?

AVRIL BENOIT: Well, you're speaking of both.

And anyone that is carrying a gun essentially that's engaged in this war, when we call for a cease-fire, when we call for respect of civilian spaces, it is imploring all the fighting parties, the warring parties to respect the call for cease-fires.

NICK SCHIFRIN: Israeli and U.S. officials consistently say that they see Hamas fighters operating from U.N. schools, even the hospitals that we have been talking about.

Have you seen Hamas fighters use these hospitals as any kind of command-and-control or the source of fire at Israeli forces?

AVRIL BENOIT: We keep hearing these allegations, without much to substantiate them, in terms of our own experience of the hospitals where we're supporting.

These are sometimes vast structures.

They do have tunnels underneath for clinicians, for health care workers who are dealing with hundreds of patients.

What we see are just hospitals that are full of patients.

And a reminder to all those who justify these massacres, these attacks on civilian infrastructures on the basis that the space was militarized, civilian spaces are being militarized by all sides in this, both sides in this.

And it's not acceptable to then suggest that the protection of civilians, which is enshrined in the Geneva Conventions, doesn't apply because you might have something going on in the vicinity that is not under the control of those who are running the hospitals, for example.

There seems to be a disregard for civilians in this conflict that is shocking.

And we would just remind all the belligerents that they should respect those spaces, not attack them, stay clear of them, so that they can deliver the aid that people need.

NICK SCHIFRIN: Avril Benoit, chief executive officer of Doctors Without Borders USA, thank you very much.

AVRIL BENOIT: You're welcome.