The rescue by Israel of four hostages being held by Hamas could highlight the logic, sketched by Prime Minister Netanyahu and the war cabinet, of Israel pressing its attack in Gaza rather than seek a cease fire. 

The rescue of the hostages after 246 days in captivity was described by authorities as a complex operation and its largest one since the war with Hamas began. The army said it freed them in a daytime operation in the heart of the Nuseirat refugee camp, raiding two locations at once while under fire. 

The hostages — Noa Argamani, 26; Almog Meir Jan, 22; Andrey Kozlov, 27; and Shlomi Ziv, 41 — were all well, the military said. They were taken by helicopter for medical checks and tearful reunions with loved ones.

Ms. Argamani had been one of the most widely recognized hostages after being taken, like the three others, from a music festival. The video of her abduction showed her seated between two men on a motorcycle as she screamed, “Don’t kill me!”

Her mother, Liora, has brain cancer and had released a video pleading to see her daughter before she dies. Israel’s Channel 13 said Ms. Argamani was moved to the hospital where her mother is being treated. Her father, Yaakov, on Saturday had his birthday. “I never believed I would receive a present like this,” he said.

In a video message released by the government, an elated Ms. Argamani told Mr. Netanyahu by phone she was “very excited,” saying she hasn’t heard Hebrew in so long.

Mr. Netanyahu in a statement vowed to continue the fighting until all hostages are freed. The operation was “daring in nature, planned brilliantly, and executed in an extraordinary fashion,” Israel’s defense minister, Yoav Gallant, said.

Neighboring Egypt condemned “with the strongest terms” Israel’s attacks on the Nuseirat refugee camp, with its foreign ministry calling it a “flagrant violation of all rules of international law.” Neighboring Jordan also condemned it.

Israel’s military said it had attacked “threats to our forces in the area,” adding that one commando died from his wounds.

An American hostage cell provided advice and support throughout the process of locating and rescuing the hostages, according to a Biden administration official, who was not authorized to comment and requested anonymity. The hostage cells are multi-agency teams.

“We won’t stop working until all the hostages come home and a cease-fire is reached,” President Biden said.

Hamas took some 250 hostages during the Oct. 7 attack that killed about 1,200 people. About half were released in a weeklong cease-fire in November. About 120 hostages remain, with 43 pronounced dead. Survivors include about 15 women, two children under five and two men in their 80s.

Saturday’s operation brought the total number of rescued hostages to seven. Two were freed in February and one was freed in the aftermath of the October attack. Israeli troops have recovered the bodies of at least 16 others, according to the government.

The latest rescue was expected to lift spirits in Israel as divisions deepen over the best way to bring hostages home. Some Israelis urge Mr. Netanyahu to embrace a cease-fire deal Mr. Biden announced last month, but others are threatening to collapse his government if he does. Mr. Netanyahu rushed to the hospital to greet the freed hostages.

It was unclear what effect it might have on apparently stalled cease-fire efforts. Secretary Blinken will return to the Middle East next week, seeking a breakthrough.

“The hostage release and cease-fire deal that is now on the table would secure the release of all the remaining hostages together with security assurances for Israel and relief for the innocent civilians in Gaza,” Mr. Biden’s national security adviser, Jake Sullivan, said in a statement.