Over 600 foreign passport holders -- nearly half of whom are Americans and Canadians -- were on a list of people approved to leave Gaza on Sunday. Some 566 foreign passport holders, whose nationalities were not released, later exited the Gaza Strip through Egypt’s Rafah border crossing on Sunday, crossing spokesman Wael Abu Omar told ABC News.

Thirteen wounded Gaza residents and 11 of their family members also left Gaza and entered Egypt on Sunday, the spokesman said.

-ABC News' Ayat Al-Tawy

The Israel Defense Forces has started a ground operation in southern Gaza that "will be no less powerful than" the operations in northern Gaza, IDF Chief of Staff Lt. Gen. Herzi Halevi said.

"We have the capabilities to do it in the most thorough way, and just as we did it with strength and thoroughly in the north of the Gaza Strip, we are also doing it now in the south of the Gaza Strip, and we also continue to deepen the achievements in the north of the Gaza Strip," Halevi said.

The IDF said it's carried out 10,000 airstrikes in the Gaza Strip since fighting began.

"The forces ‘closed circles’ and thwarted terror cells, terror infrastructure, operational apartments, tunnel shafts, weapons warehouses and more,” the IDF said in a statement.

-ABC News' Dana Savir

With the temporary Israel-Hamas cease-fire now over, National Security Council spokesman John Kirby told ABC News' "This Week" that the U.S. is "working at this literally by the hour … if we can get these discussions back going" to get a new pause in place.

Kirby said the Israel-Hamas agreement "fell apart because Hamas was unwilling and refused to come with additional [hostage] lists of women and children -- which we know they are holding -- and put them on the list so that Israel can evaluate that and we can get them exchanged."

Kirby said the U.S. thinks "about eight" Americans remain hostage.

He added, "We don’t have perfect visibility on where they all are, we certainly don’t have perfect visibility on their physical or mental condition."

6:03

Israel ‘receptive’ to US messaging on minimizing civilian casualties: John Kirby

When asked Sunday about The New York Times report alleging Israel knew about Hamas' attack plan a year in advance, Kirby said the U.S. had no knowledge of the Hamas planning document.

He added, "The focus has got to be on making sure Israel has what it needs to go after Hamas leadership."

The United Nations said 138,000 liters of fuel entered Gaza on Saturday -- the highest amount in one day since the Israel-Hamas war began.

Trucks with food, water, medicine and medical supplies also entered Gaza on Saturday, according to the U.N. Office for the Coordination of Humanitarian Affairs.

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