Israel’s government will begin voting to approve a hostage deal with Hamas on Tuesday, an Israeli senior political source told ABC News.

Voting will likely be completed on Wednesday, according to the source.

The office of Israeli Prime Minister Benjamin Netanyahu announced Tuesday that, "in light of the developments regarding the release of our abductees," Netanyahu will convene the war cabinet at 6 p.m. local time, the political-security cabinet at 7 p.m. local time and the full government at 8 p.m. local time.

Both cabinets would have to approve a hostage deal before it could be brought to the full government for a final vote.

Earlier Tuesday, while visiting Israeli troops, Netanyahu told reporters that his government was "making progress" on an agreement with Hamas.

"I don't think it's worth saying too much, not even at this moment,” he added, "but I hope there will be good news soon."

-ABC News' Victoria Beaulé, Jordana Miller and Morgan Winsor

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

Hundreds of patients are trapped inside another major hospital in the Gaza Strip amid fierce fighting between Israeli forces and Hamas militants, as fears grow that the situation could turn into a repeat of what happened at Al-Shifa Hospital.

The Indonesian Hospital is located in the northern edge of north Gaza, right on the frontline of Israel's advance. Al Jazeera reported that there are 700 people currently stuck inside the besieged hospital, including medical staff and wounded civilians.

At least 12 people, including patients and their companions, were reportedly killed on Monday when the Indonesian Hospital came under fire, according to the World Health Organization, which said it was "appalled by the attack." Doctors in the hospital told Al Jazeera that the facility was hit by artillery shells, while others suggested an Israeli tank may have fired at it.

"Health workers and civilians should never have to be exposed to such horror, and especially while inside a hospital," WHO Director-General Tedros Adhanom Ghebreyesus wrote in a post on X, the social media platform formerly known as Twitter.

Dr. Marwan Al-Sultan, director of the Indonesian Hospital, told BBC News that Israeli troops were only about 20 meters (66 feet) away. The Israeli military said its forces targeted "terrorists" who had opened fire at them from within the hospital, according to BBC News.

ABC News has not confirmed that Israeli troops were responsible for strikes on the Indonesian Hospital. The Israel Defense Forces said it was operating in specific areas outside the hospital due to enemy fire and that no shells were launched toward the facility.

Gaza's Hamas-controlled Ministry of Health said 200 patients were evacuated from the Indonesian Hospital by bus to southern Gaza and that the International Committee of the Red Cross was trying to coordinate the evacuation of the remaining 400 patients, according to BBC News.

Video purportedly taken inside the Indonesian Hospital shows injured people and others sheltering on the floor. Additional footage appears to show damage to the hospital and heavy bombardments landing close to the facility in recent days.

-ABC News' Patrick Reevell, Kerem Inal and Morgan Winsor

A little more than 1,200 Americans and their eligible family members are waiting to leave Gaza, according to State Department spokesperson Matt Miller.

About 800 Americans and eligible family members have already left Gaza, Miller said.

Since the Israel-Hamas war broke out on Oct. 7, another six Americans have died: one was an Israeli national police border officer and five were members of the Israel Defense Forces, Miller said. At least 33 Americans were killed in Israel on Oct. 7 during Hamas' attack, according to American officials.

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How to help victims of the Israel-Gaza conflict

More than 2,600 people, including civilians and hundreds of children, have been killed and nearly 9,000 injured in Israel and Gaza since the war broke out on Saturday.

-ABC News' Shannon Crawford