"The Islamic Resistance Movement Hamas is seeking to extend the truce after the end of the four-day period, by seriously considering increasing the number of released detainees as stated in the humanitarian truce agreement," Hamas said in a statement Sunday.

The AFP news agency reported that a source close to Hamas said the group also informed mediators of its willingness to extend the current truce.

-ABC News' Ayat Al-Tawy

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."

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

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