Hostage negotiations to free many of the 200-plus people believed to be held by extremists in Gaza have "reached a very sensitive stage" as some key areas of disagreement preventing a deal have "narrowed," a top White House official said Sunday, suggesting a breakthrough could be imminent but not certain.
"These talks have clearly reached a very sensitive stage," President Joe Biden's deputy national security adviser, Jon Finer, told ABC "This Week" co-anchor Martha Raddatz.
"We're following this minute by minute, hour by hour, and have been over a number of weeks," Finer said. "And this is an incredibly high priority for all of us in this administration up to and including, certainly, the president."
Amid new reporting that an agreement is on the verge of being struck for a large number of the captives in exchange for a potentially dayslong pause in the fighting sparked by Hamas' Oct. 7 terror attack on Israel, Finer said "significant progress" had been made as recently as this weekend.
But he cautioned that the work was not done.
"[S]ome of the gaps have now narrowed. Some of the issues that were at odds have now been closed out. But we are not finished -- there is not yet a deal in place. And I think it would be premature to conclude that this is inevitable given how close we have come in the past," he said.
Michael Herzog, the Israeli ambassador to the U.S., echoed that view in his own interview with Raddatz.
"The less we're going to the details, the better the chances of such a deal. But they are very serious efforts and I'm hopeful that we can have the deal in the coming days," he said.
MORE: 'I'm afraid': War stories from children caught in the middle of the Israel-Hamas conflictIsrael and Hamas have been locked in fierce fighting since Hamas launched its attack from Gaza on southern Israel on Oct. 7, killing more than 1,200 people and taking more than 230 hostages, according to Israeli officials.
Talks over freeing those captives -- who represent multiple nationalities, with Americans among them -- have progressed with the involvement of intermediaries like the government of Qatar.
When pressed on how many hostages could be released, Finer said "certainly more than dozens." He also said that while the U.S. doesn't "have perfect clarity" on the state of the hostages, officials believe most of them, "even the vast majority," are still alive.
To facilitate their freedom, Finer said the U.S. would be open to "a much more extended period of pause" -- but not a cease-fire.
"That would also make it much easier to both bring humanitarian assistance into Gaza and also distribute that assistance throughout Gaza," Finer said.
Israel has bombarded the Palestinian territory in the month since Hamas' attack and casualties have been high, with 12,300 people killed in Gaza, according to the Hamas-run Gaza Health Ministry.
Humanitarian workers, including those with the U.N., have warned of mounting catastrophe in Gaza if more aid isn't allowed in and if Israel doesn't curb its military campaign.
Herzog, in his "This Week" appearance, indicated Israel would not agree to a full cease-fire until Hamas is annihilated.
"Our intention is to dismantle the Hamas terror machine," he said.
Raddatz pressed Herzog on the death toll so far. He acknowledged "collateral" damage in the fighting and insisted, "Every loss of human life, Israeli or Palestinian, is a tragedy. We are not after innocent civilians. We are after the terrorists who have been hiding behind civilians."
He also challenged the statistics being released by Hamas-affiliated groups in Gaza.
"Nobody really knows how many people died there," Herzog said, though he added, "There's no denying that there's collateral, that the civilians died."
"I don't know how many of them are terrorists and how many of them are civilians. Nobody really knows," he said.
Finer, separately, said the U.S. believes a cease-fire is also not tenable right now because Hamas wants to keep attacking Israel.
"We totally don't accept that," he said.
All the while, conditions in Gaza are worsening, with a school recently reportedly hit by shelling and worries around conditions at the Shifa Hospital, the largest and most advanced such facility in Gaza, which Israeli forces recently raided, believing that Hamas was using it as a command and military center.
The terrorist group and hospital workers deny that, but both Finer and Herzog said on "This Week" that Israel and the U.S. think otherwise.
"We found a lot of weapons. We found computers. We found a lot of things. We found tunnels," Herzog maintained. "We're now searching these tunnels. They're all booby trapped. But we are in the process of searching these tunnels and we'll show our findings to the world."
Nonetheless, Finer said, Israel has an obligation to protect civilians even in the trickiest circumstances.
"That is the box that Israel finds itself in. And it finds itself there largely because Hamas has chosen to use a hospital as a place from which to fight," he said.
Herzog said Israel had taken steps to help Shifa Hospital continue to operate and to evacuate some of its most vulnerable, such as babies who are patients there.
But outside aid workers have painted a dire picture of what is happening on on the ground.
"From all accounts, the situation in Shifa sounds desperate, and there are still a large number of people in a critical situation in that hospital," Thomas White, the Gaza director for the U.N. agency for Palestinian refugees, told Raddatz in an interview from Rafah, Gaza.
"The situation is still very desperate, and of course the fighting rages in the north," White said. "And once again, we have horrific scenes coming out of one of our schools that was hit during that fighting, a large number of people killed. We're still trying to verify the information from up there. It's very clear it is a [U.N.] school. And so the death toll continues to mount and these are people sheltering inside of a school."
More broadly, "the reality of this conflict is that people in Gaza have got nowhere to go," White said. "It's unlike other conflicts where, you know, there's fighting in one city and you move to another city. In Gaza there is nowhere to go."
Thirteen U.N. shelters have been "directly hit" during the war and nearly three dozen others had taken some damage, White said.
"The reality of this conflict is that people in Gaza have got nowhere to go," he said. "It's unlike other conflicts where, you know, there's fighting in one city and you move to another city. In Gaza, there is nowhere to go."
"Increasingly, people are very worried about -- what's the future hold for them [in Gaza]?" he said. "Where are they going to live? Where are they going to get their children educated? What does the future hold? And that's the big question."
Israeli Prime Minister Benjamin Netanyahu previously told ABC News anchor David Muir that, after the war, Israel planned to resume security control of Gaza for "an indefinite period," though the U.S. has publicly reiterated that they do not want Israel that involved in the Palestinian territories.
Herzog said Sunday that "to reoccupy Gaza, to govern Gaza, it is not our desire. It is not our wish. We do not wish to take territory from Gaza."
"We are in the dialogue with United States about [what comes] after Hamas in Gaza," Herzog said, "and that includes, of course, the idea that Palestinians will govern over Palestinians."