Alma Avraham, an 84-year-old Israeli hostage freed by Hamas on Sunday, remains hospitalized in critical condition, Israeli officials said Monday.

She suffers from preexisting conditions and was receiving regular medication before she was kidnapped, said Dr. Tzachi Slotsky, deputy administrator of Soroka Medical Center.

"If she hadn’t been transferred to us yesterday, or any other delay in her transfer, it would’ve worsened her condition even more," Slotsky said. "She is intubated and sedated at the emergency room and her life is still in danger."

Without care, she soon would have died, said Avraham's daughter, Tali Amano.

"My mother did not deserve to return this way -- my mother was medically neglected," Amano said. "She didn’t get any of her medication."

"The only reason we are standing here today ... is to save those who are left there [in Gaza]," Amano said.

-ABC News' Jordana Miller and Morgan Winsor

The family of 4-year-old hostage Abigail Idan has released the first photo of the little girl following her return home from Gaza.

Abigail, an American-Israeli citizen, had been held hostage by Hamas since Oct. 7. She was released on Sunday, two days after her 4th birthday.

Abigail Idan’s aunt, Ella Mor, said in a video Sunday, "She just landed in the hospital and she’s being checked and taken care of."

"I'm so happy that she's here," Mor told ABC News. "The people of Israel are amazing … everybody's so happy like she's their own little girl."

Israel has taken issue with the list of hostages that Hamas said it would release on Monday because it includes children without their mothers, an Israeli source told ABC News.

However, the source said there is optimism that the issue will be resolved by Monday night and an extension to the four-day truce, set to expire Tuesday morning, will be approved.

The Israeli Prime Minister's Office confirmed in a statement that negotiations with Hamas on Monday's hostage list "are continuing."

-ABC News' Jordana Miller and Morgan Winsor

Egypt's State Information Service (SIS) announced Monday that Egyptian-Qatari mediation between Israel and Hamas is close to reaching an agreement to extend a four-day truce by two days.

The deal would also involve the release of 10 Israeli women and children being held hostage by Hamas in the Gaza Strip in exchange for 30 Palestinians detained in Israeli prisons each day of the extension, totaling 20 Israeli hostages and 60 Palestinian prisoners, according to SIS chairman Diaa Rashwan.

A cease-fire, the halt of air raids as well as the entry of aid and fuel into war-torn Gaza would continue during the additional two days of the truce, Rashwan said.

Rashwan also said that the fourth group of releases Monday would include 11 Israelis and 33 Palestinians.

-ABC News' Ayat Al-Tawy and Morgan Winsor

The United States will send three relief flights into Egypt on Tuesday to keep up the flow of humanitarian aid into the war-torn Gaza Strip, which has reached its highest levels as officials take advantage of the current humanitarian pause.

"The movement over the last four or five days of assistance has been so significant in volume that a backfill in El Arish [International Airport in Egypt] is now needed, and these planes are part of that backfill," a senior Biden administration official told reporters during a telephone call on Monday afternoon.

Some 800 trucks carrying aid have crossed into Gaza during the first days of the pause, officials said, which is a huge increase from the days prior. So far, a total of about 2,000 aid trucks have entered Gaza since Oct. 7, meaning that 40% of them had gone in in just the last four days.

The planes on Tuesday will be carrying medical aid urgently needed in Gaza as well as food, particularly for children, and winter clothing as the rainy season begins, according to officials.

The aid will be delivered by the United Nations to civilians.

Two more planeloads are expected to follow in the coming days, officials said. Previously, there were also five commercial flights of aid coordinated by the U.S. government, according to officials.

The officials emphasized this aid as part of U.S. President Joe Biden’s commitment to helping the Palestinian people, saying that he has made sure America is the largest single donor both to the United Nations Relief and Works Agency for Palestine Refugees in the Near East (UNRWA) and to Palestinian territories.

Going forward, the officials said the goals for humanitarian aid in Gaza will be expanding access, pushing for restoration of essential services, especially water, and keeping civilians out of harms way.

"The president has also consistently stressed the importance of ensuring military operations are conducted in a manner consistent with international humanitarian law, including with respect to the protection of civilians," the senior Biden administration official told reporters.

Officials did not offer any new information on the hostage negotiations between Gaza's militant rulers, Hamas, and Israel but reiterated that they hope to see Americans released in the coming days.

-ABC News' Cheyenne Haslett and Morgan Winsor