At least 274 people were killed in central Gaza on Saturday as the Israeli military moved into the Nuseirat camp to rescue four hostages, the Hamas-run Gaza Health Ministry said Sunday.

Another 698 people were injured as Israeli forces entered the refugee camp, the ministry said.

Some of the injured were in critical condition, the ministry said.

The death toll in Gaza climbed on Saturday to 37,084 people, the ministry said. More than 84,000 others have been injured, the ministry said.

-ABC News’ Victoria Beaule and Kevin Shalvey

U.S. Central Command (USCENTCOM) announced Saturday that it began delivery of humanitarian assistance ashore in Gaza.

"Today, a total of approximately 492 metric tons (~1.1 million pounds) of much needed humanitarian assistance was delivered to the people of Gaza," CENTCOM said in a statement.

No U.S. personnel went ashore to Gaza, according to CENTCOM.

The agency said it has so far assisted in the delivery of more than 1,573 metric tons of humanitarian aid to organizations operating on the ground in Gaza.

-ABC News' Nathan Luna

Secretary of State Antony Blinken released a statement Saturday following the rescue of four Israeli hostages, welcoming their safe return.

"The United States will not rest until every hostage is returned home," he said.

Blinken also pushed for the cease-fire announced last week by President Joe Biden.

He contended would "bring relief to both the people of Gaza and the remaining hostages and their families through an immediate ceasefire that could lead to the release of all hostages, a surge of humanitarian assistance, Gaza’s reconstruction, and an enduring end to the war."

"The only thing standing in the way of achieving this ceasefire is Hamas. It is time for them to accept the deal," he said.

A U.S. defense official provided ABC News with some more details about the operation.

The official said the recently constructed JLOTS pier, which is used for transporting humanitarian supplies, was not used in the operation.

"An area south of the facility was used to safely return the hostages to Israel. Any such claim to the contrary is false," the official said.

-ABC News' Nathan Luna

After meeting with rescued hostages and their families, Israeli Prime Minister Benjamin Netanyahu called the rescue operation "remarkable" and told reporters they will do "whatever it takes" to get the hostages back.

"We're committed to getting the release of all the hostages, and we expect Hamas to release them all — but if they don't, we'll do whatever it takes to get them all back home. Hamas is committing war crimes every day, including the holding of these hostage.s. Our soldiers are performing in the most valiant and moral way to end this war with a victory against these killers and against these kidnappers, and we shall prevail," Netanyahu said.

Earlier, the Israel Defense Forces said the hostages were being held in civilian populated areas, without any way to reach them but go through Gaza civilians, IDF spokesman Daniel Hagari told reporters. Three male hostages were held together in an apartment and a fourth female hostage was held in another apartment just over 650 feet away, Hagari said.

At least 150 Palestinians were killed in Israeli raids on Saturday, the Hamas-run Gaza Health Ministry said.

A United States official provided ABC News with more details about the rescue efforts, noting that the U.S. has been providing regular intelligence sharing and expertise on hostage recovery efforts since Oct. 7.

The official stressed there were no American boots on the ground as part of this effort.

-ABC News' Dana Savir, Bruno Nota and Molly Nagle

President Joe Biden outlined Israel’s cease-fire proposal accurately in his Friday speech, the White House maintained Monday, pushing back on suggestions he miscommunicated the offer.

"The Israeli foreign minister himself acknowledged that this was the Israeli proposal ... and we're confident that it accurately reflects that proposal, a proposal that we worked with the Israelis on," White House national security communications adviser John Kirby told reporters.

Kirby also argued that Biden "felt it was important" to reveal details from ongoing cease-fire negotiations for the first time, saying it was meant to apply pressure on Hamas, not to corner Israeli Prime Minister Benjamin Netanyahu.

"We don't typically go through the details of these kinds of proposals," Kirby said. "But in this case, given where we are, given how much longer the hostages have now been held, given the fact that Hamas has reneged on several past occasions, on proposals that were sent to them, and given the fact that the Israelis really did work hard to come up with this proposal, and did so in good faith, the president felt it was important for the first time to publicly lay that out."

"This wasn't about jamming the prime minister or the war cabinet," Kirby added. "This was about laying bare for the public to see how well and how faithfully and how assertively the Israelis came up with a new proposal, how it shows how much they really want to get this done."

Kirby said Biden delivered the speech on Friday afternoon because the deal was presented to Hamas the night before.

"We're awaiting an official response by them now to take the deal," Kirby said. "This gives them what they've been looking for, which is a cease-fire and over time, and through the phases, the potential withdrawal of Israeli forces from Gaza."

-ABC News’ Fritz Farrow