President Joe Biden spoke with Israeli Prime Minister Benjamin Netanyahu on Sunday about the latest developments in Gaza, including the release of more hostages, the White House said.

"The President welcomed the release of hostages by Hamas over the past three days, including a young American girl. The two leaders also discussed the pause in the fighting and surge in much needed additional humanitarian assistance into Gaza," the White House said.

The Israeli prime minister's office also issued a statement following their conversation, saying they spoke with "great excitement" about the hostages who were released, including 4-year-old Abigail Idan.

"What a joy to see her with us. But on the other hand, what a pity that she returns to the reality of not having parents. She has no parents -- but she has a whole nation that embraces her and we will take care of all her needs," Netanyahu's office said.

-ABC News' Justin Ryan Gomez

Alma Avraham, an 84-year-old Israeli hostage released by Hamas Sunday, was taken to Soroka Medical Center in Beersheba in "serious condition," IDF spokesman Daniel Hagari said.

"Alma, who was returned to us in serious condition, was immediately evacuated by helicopter to the hospital. She was evacuated by IDF troops while still inside Gaza,” he said during a press conference.

Due to "medical reasons" and to ensure the safety of the hostages, 13 of them were escorted out of Gaza by special forces near the community of Be'eri, "in full coordination with Egyptian security authorities," Hagari added.

In a short statement, Soroka said Avraham is in "poor physical condition and severe clinical condition."

The IDF and General Security Service killed five senior Hamas officials in Gaza, IDF spokesman Daniel Hagari said Sunday, adding they were "key figures and key partners" in the Oct. 7 attack.

Hagari also said the war will not end until all the hostages are returned.

"This is the ethical and moral duty of every IDF soldier and the bodies of the defense establishment," he said.

Israeli Prime Minister Benjamin Netanyahu toured the Gaza Strip on Sunday and vowed the return of all of the hostages taken by the Hamas terror group, according to the prime minister's office.

Netanyahu spent time with Israeli commanders and fighters and visited one of the Hamas tunnels uncovered by Israeli forces, the prime minister's office said in a statement.

"We are here in Gaza with our heroic fighters," Netanyahu said in a video released by his office showing him wearing a helmet and flak jacket, and surrounded by Israeli soldiers. "We make every effort to return our abductees, and eventually we will return them all. We have three goals for this war: eliminate Hamas, return all our abductees, and ensure that Gaza does not become a threat to the State of Israel again."

Netanyahu added, "We continue until the end -- until victory. Nothing will stop us, and we are convinced that we have the power, the strength, the will and the determination to achieve all the war's goals, and we will."

-ABC News' Bruno Nota and Jordana Miller

Negotiations to free some of the people who were taken hostage by Hamas during the Oct. 7 attack on Israel are closer than they have ever been before, according to Qatari Ministry of Foreign Affairs spokesperson Majed Al-Ansari.

"Mediation has reached a critical and final stage and has gone past key issues. What remains are limited issues and therefore we are the closest we have come to reaching an agreement since the beginning of this crisis," Al-Ansari said during a press briefing in Doha on Tuesday, adding that "we hope and seek to make this happen soon."

Al-Ansari noted that it is very important to "choose the right time to announce the details" of Qatar's mediation efforts in the latest outbreak of war between Israel and the Gaza Strip's militant rulers, Hamas.

A Hamas leader in Beirut, Osama Hamdan, told ABC News on Tuesday morning that they are "waiting for the Israeli side to accept the deal." However, he added a caveat: "Many times in the past, we were close to a deal and Netanyahu undermined the deal. By the end of the day things will clear and we will see what the results of it."

Hamdan would not expand on details of the deal, including how many hostages would be released, telling ABC News: "No specifics on the numbers but it's around what the media is talking about, which is around 50. But nothing is final."

Meanwhile, there will likely be three separate steps of approval for an agreement to go through on the Israeli side. The Israeli government will announce that a deal has been reached that needs to be voted on. Then, Israel's security cabinet will vote to approve said agreement. Finally, Israeli law requires a 24-hour waiting period during which time the Supreme Court of Israel may need to be involved, to defend the deal from anyone who attempts to contest it.

Sources have told ABC News that a potential deal would involve the release of around 50 hostages, all women and children, in exchange for a five-day cease-fire, the release of dozens of Palestinian women and children from Israeli prison and a large influx of humanitarian aid into Gaza, including fuel. It may take multiple days for hostages to be released because they are not all being held together and some are held by splinter groups, according to sources.

-ABC News' Ayat Al-Tawy, Nasser Atta, Victoria Beaulé, Matt Gutman, Jordana Miller, Kirit Radia and Morgan Winsor