Israeli Prime Minister Benjamin Netanyahu said Wednesday evening that "there will be no cease-fire without the release of our hostages -- everything else is false."

National Security Council spokesman John Kirby said there are about 500 to 600 Americans and family members remaining in Gaza.

Asked if the lack of humanitarian pauses is a factor in why hundreds of Americans remain in Gaza, Kirby said it’s among the many "complicating factors."

Kirby would not confirm Axios' report that President Joe Biden is asking Israeli Prime Minister Benjamin Netanyahu for a three-day pause to allow progress in releasing more hostages, but Kirby said that discussions are ongoing with Israel, noting that there have been pauses in the past.

Kirby said they are trying to get an agreement "for as many pauses as might be necessary to get all of them out," but called it a "delicate negotiating process," and laid out some of the options that are being floated.

"What we're talking about here is temporary, fixed in time, short duration, hours to days, depends on the need. And then also localized in terms of the map," he explained. "So it would be an agreement that for a set period of time [in a set area] there will be a pause in the fighting. That doesn't mean that there won't be or couldn't be fighting outside that zone during that same period of time. So all of that has to get factored in and I have no doubt that on the Israeli side, as they look at each proposal, they'll think about the impact, potential impact, on their military operations on the ground or in the air."

-ABC News' Justin Ryan Gomez

Over one month since Hamas took more than 200 people hostage in Israel, National Security Council spokesman John Kirby said the administration is still "not aware of any specific proof of life."

"We don't have any indication to the contrary, that they aren't still alive. And so, we're certainly operating under that assumption," he said.

"We don't have a perfect picture about where everybody is, what condition they're in, or how they're being held," Kirby continued. "We cannot rule out the possibility that other groups than Hamas may have hostages that they're holding."

-ABC News' Justin Ryan Gomez

United Nations High Commissioner for Human Rights Volker Turk said both Hamas and Israel have committed war crimes since Oct. 7.

"The atrocities perpetrated by Palestinian armed groups on 7 October were heinous, they were war crimes -- as is the continued holding of hostages," Turk said.

"The collective punishment by Israel of Palestinian civilians is also a war crime, as is unlawful forcible evacuation of civilians," he added.

During brief remarks in New Delhi Friday morning, U.S. Secretary of State Antony Blinken swiftly acknowledged the Biden administration’s “appreciation” of Israel’s commitment to four-hour pauses with three-hour notice in specific areas and corridors of Gaza “that will allow people to move more safely, freely to get out of harm's way and also to access assistance.”

“At the same time, much more needs to be done to protect civilians and to make sure that humanitarian assistance reaches them," he continued. "Far too many Palestinians have been killed. Far too many have suffered these past weeks, and we want to do everything possible to prevent harm to them, and to maximize the assistance that gets to them.”

The secretary said they have established basic principles to guide the effort for lasting peace and security in the region: no use of Gaza as a platform for launching attacks against Israel, no diminution in the territory of Gaza and a commitment to Palestinian-led governance.

Blinken reaffirmed that the administration had “long been committed” to a two-state solution, and the terror attacks of Oct. 7, he said, only redouble American commitment to the peace process.

“But now we've had the events of October 7 -- the almost, beyond the human imagination -- horror of October 7. And I think that only reinforces us in our conviction and our commitment to durable and lasting peace which again, we see through two states,” he said.

On humanitarian assistance, Blinken said that “more than plans, we have a concrete way forward,” including ensuring that there are adequate supplies of fuel for the trucks coming in and that hospitals and desalination plants “have what they need.”

“It's always a process and moving from an understanding, moving from an agreement to implementation is what we're working on right now,” he said.