Negotiations to free the more than 200 hostages believed to be held by Hamas in Gaza have "reached a very sensitive stage" as some of the key areas of disagreement have "narrowed," a top White House official told ABC's "This Week" on Sunday.

Jon Finer, deputy national security adviser to the White House, suggested that a breakthrough in the negotiations could be imminent.

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Some ‘gaps’ have ‘narrowed’ in Israel-Hamas talks: Jon Finer

ABC News’ Martha Raddatz interviews White House Deputy National Security Adviser Jon Finer on “This Week.”

"These talks have clearly reached a very sensitive stage," Finer told "This Week" co-anchor Martha Raddatz. "We’re following this minute by minute, hour by hour, and have been over a number of weeks. And this is an incredibly high priority for all of us in this administration up to and including, certainly, the president."

Amid new reporting by The Washington Post that an agreement is on the verge of being struck for dozens of captives to be released in exchange for a pause in the fighting, Finer said progress was being made but cautioned that the work was not done.

-ABC News' Tal Axelrod

Humanitarian officials with the United Nations described the situation inside Gaza's Al-Shifa hospital as "desperate" and "a death zone" after they visited the site on Saturday.

The World Health Organization, a U.N. agency, said there was "heavy fighting" ongoing nearby. The Israeli military deconflicted the fighting during a one-hour visit to the hospital, WHO officials said.

"Signs of shelling and gunfire were evident," the WHO said in a statement. "The team saw a mass grave at the entrance of the hospital and were told more than 80 people were buried there."

The corridors and hospital grounds were "filled with medical and solid waste," WHO officials said. They described the staff as terrified and said patients "pleaded for evacuation."

Due to the conditions, the WHO are now working "urgently" to develop plans to evacuate the remaining patients and staff.

-ABC News' Guy Davies

In a sit-down interview with ABC News in Beirut on Saturday, Osama Hamdan, a senior official with Hamas in Lebanon, said the goal of the Oct. 7 attack was to show Israel and the world that the "Palestinian cause is still alive."

He said he believes that the operation has worked to that end.

"The United States start to talk about the rights of the Palestinians. All the world starts to talk about the rights of the Palestinians," he said.

Despite eyewitness accounts, news reports and video evidence, Hamdan denied that Hamas killed innocent people at a music festival in southern Israel on Oct. 7 or that they took civilian hostages from Israel. Hamdan claimed that Hamas militants only took military "prisoners," and that civilian hostages were taken by other groups. He said Hamas is willing to release hostages -- but only if Israel agrees to a cease-fire.

More than 260 bodies were recovered from the musical festival following the attack, Israeli officials said. At least 1,200 people total were killed in Israel and nearly 240 people were taken hostage in the Oct. 7 attack, Israeli officials said.

Asked if Hamas bears any responsibility for the deaths of thousands of innocent Palestinians, Hamdan said "it may take more sacrifices" but that more lives could be saved "by forcing Israel to recognize the rights of the Palestinians, to leave the occupied lands" and to let Palestinians determine their future.

-ABC News' Bruno Roeber, Ghazi Balkiz and Marcus Moore

Dozens of people were killed on Saturday in air strikes on a refugee camp in Gaza, according to the Hamas-run Gaza Health Ministry.

At least 50 people were killed in an Israeli strike on the al-Fakhouri school in the Jabalia refugee camp, the health ministry said.

Another Israeli strike on a separate building in the camp killed 32 people -- including 19 children -- all from the same family, according to the health ministry.

ABC News has not been able to independently verify the claims and those numbers have yet to be corroborated.

The school, which is run by the United Nations Relief and Works Agency for Palestine Refugees (UNRWA), is currently serving as a shelter for thousands of displaced Palestinians, the agency said.

The commissioner general of UNRWA said Saturday he had received footage of "scores of people killed and injured" at the school.

The Israel Defense Forces said in a statement it had received reports of an "incident in the Jabalia region," which is under review.

"Despite the challenges posed by terrorists operating within civilian areas in Gaza, the IDF is committed to international law including taking feasible steps to minimize harm to civilians," the statement said.