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.

Through tears and voices choked with raw emotion, people whose family members are believed to held hostage by Hamas pleaded for help during a Republican-led press conference at the U.S. Capitol on Tuesday.

Doris Liber told reporters that her son, Guy Iluz, called her as Hamas unleashed its terrorist attack against Israel on Oct. 7 and she hasn't heard from him since.

"I'm here because it's been 30 days. Every day is like eternity to me," Liber, who holds joint Israeli-American citizenship, said. "We don't have a list of the hostages. We don't know their condition. I don't have anything. So I need your help."

She described the last time she spoke to her son.

"We hear shots in the background," she said. "He was shot in the arm and he wasn't able to stop the bleeding and he was trying to say his last words."

“I tried to, you know, tell him, ‘Guy I love you. Don't worry, nothing's going to happen. I'm going to end the call now. I'm going to send somebody now to get you,'" she continued. "And that's what I did. I hung up and I regret that since I didn't hear from him since."

Yonatan Lulu-Shamriz said he was awoken by his pregnant wife as the sirens began to sound in their kibbutz. They grabbed their 3-year-old daughter, huddled in a safe room and listened as their neighbors were slaughtered, he said. Soon his brother, Alon, called to report he was under attack, Lulu-Shamriz said.

“We don't know what is their condition," Lulu-Shamriz said. "This is a wake-up call not only for Israel, not only for the Jewish community. This is a wake-up call for all of you -- all of you here, all of America, all of Europe. You are next. You are next. And we should do everything that we can to stop these atrocities."

House Speaker Mike Johnson vowed to "take action."

"We're resolved to help," the newly minted speaker said. "House Republicans want to do that."

-ABC News' John Parkinson and Lauren Peller