Israel-Gaza updates: Israel says ground operation underway in southern Gaza

White House National Security spokesperson John Kirby said there's no indication that Hamas is trying to keep Americans as hostages in order to use them as leverage.

"There's no indication that Hamas is trying to play some sort of game here in terms of the Americans," Kirby told reporters Tuesday.

He added that the first test case of getting hostages out involved two Americans, including a teenager from the Chicago area, and that 4-year-old American-Israeli hostage Abigail Idan was released over the weekend.

In the latest exchange on Tuesday, 12 hostages -- 10 Israelis and two foreign nationals from Thailand -- were released, the Israeli government said.

Kirby reiterated that the pool of American hostages is "pretty small, and the pool of Americans that qualify right now, women and children, is smaller still."

He also noted that there are issues locating the hostages, who may be held by various groups.

The U.S. believes there are eight or nine Americans still being held in Gaza, Kirby said on Monday.

-ABC News' Selina Wang and Cheyenne Haslett

Releasing more hostages will be a "prime" focus of Secretary of State Antony Blinken's latest trip to the Middle East, the White House said.

"We're up around 70 or so hostages out so far, which is good. It's a good start, but it's just a start. There are many more," White House National Security spokesperson John Kirby told reporters Tuesday. "We want to get them all back."

Blinken will also meet with his Israeli counterparts to reassure them of U.S. support and talk about getting humanitarian assistance to Gaza, Kirby said.

This week's trip will be Blinken's fourth to the region since the Oct. 7 attack.

-ABC News' Cheyenne Haslett

The United States delivered more than 54,000 pounds of medical and food aid for Gaza in a flight to Egypt earlier Tuesday, according to National Security Advisor Jake Sullivan.

Two more planes are set to make deliveries in the coming days, he said.

"The humanitarian needs in Gaza demand that the international community do much more," Sullivan continued, adding that the U.S. is committed to keeping that aid up.

-ABC News' Cheyenne Haslett

Twelve hostages are back in Israeli territory in the latest exchange, according to the Israeli government.

The hostages include 10 Israelis and two foreign nationals, both from Thailand, officials said.

The Israeli citizens were identified as Tamar Metzger, 78; Ditza Hayman, 84; Norlin Babdila, 60; Ada Sagi, 75; Ophelia Edith Roitman, 77; Rimon Kirsht, 36; Merav Tal, 53; and the Leimberg family -- Gabriella Leimberg, 59, Mia Leimberg, 17, and Clara Marman, 63.

The IDF said the hostages were taken through Egypt before heading to a meeting point in Kerem Shalom, in Israel.

Five of the women -- Metzger, Hayman, Ada Sagi, Roitman and Tal -- were residents of Kibbutz Nir Oz, one of the communities hit hardest by Hamas' Oct. 7 attack.

"They were held captive, in harsh conditions and deprived of essential medical care. Two of the women released have been separated from their husbands, who remain in captivity," the kibbutz said in a statement. "The Nir Oz community is committed to support them, and their families, through the long recovery process ahead."

Thirty Palestinian prisoners were released in exchange for the hostages, according to Qatari officials.

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12 more hostages released after extended Israel-Hamas cease-fireThe hostages include 10 Israelis and two foreign nationals.

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-ABC News' Will Gretsky