Aides said the president was also hopeful that the hostage release could be an early step toward a broader peace in the region once the immediate crisis ends. In an opinion article published in the Washington Post on Sunday, Mr. Biden described how far his ambitions stretch beyond the four-day pause in fighting agreed to on Tuesday.
“Our goal should not be simply to stop the war for today,” he wrote. “It should be to end the war forever, break the cycle of unceasing violence, and build something stronger in Gaza and across the Middle East so that history does not keep repeating itself.”
Mr. Biden and his top aides have repeatedly said they do not tell Israel how to respond to the slaughter of 1,200 people inside their country, and Mr. Netanyahu made it clear on Tuesday that he intended to resume military operations against Hamas as soon as the hostages were freed in accordance with the deal.
“The war will continue,” Mr. Netanyahu said.
But some senior American officials have signaled they would not be disappointed if the pause became a more permanent cease-fire. If the White House tries to use the hostage deal to press for a longer-term cease-fire and start moving toward the bigger questions about occupation and a two-state solution, that could put Mr. Biden on another collision course with Mr. Netanyahu when the fighting is scheduled to resume.
A top administration official, who briefed reporters on Tuesday in the hours before the deal was finalized, said the pause in fighting was a step toward an eventual push for peace. But the official cautioned that such a possibility was a long way off.
The official spoke on condition of anonymity to discuss a deal that had not yet been finalized.
In the short term, the president and his aides say they are focused on ensuring that Hamas lives up to the promises the militant group made during weeks of negotiations that often seemed destined to fail.
The first sign of progress came in late October, when U.S. officials received word through intermediaries in Qatar and Egypt that Hamas could accept a deal to release women and children. In return, they wanted Israel to free Palestinian prisoners, pause the fighting, and delay a ground invasion.
With Israeli troops massing outside Gaza, officials in Israel and the United States debated whether to accept the deal. Israeli officials did not think Hamas was serious about the offer and refused to delay the ground offensive. Hamas refused to provide any proof of life about the hostages. Negotiations stalled.
At the White House, Mr. Biden and his foreign policy team kept pressing. On Nov. 14, hope swelled again after Mr. Netanyahu called the president to say he could accept the latest offer from Hamas. But just hours after the call, Israeli military forces stormed Al-Shifa Hospital in Gaza, which they said served as a Hamas command center. Suddenly, communications between Hamas and the officials in Qatar and Egypt went silent. When Hamas resurfaced hours later, they made it clear: The deal was off.
For several days, the militant group demanded that Israeli troops withdraw from the hospital, which Israel refused. It took several days for the talks to resume, following a call from Mr. Biden to the emir of Qatar.
Administration officials continued pressing Israel and, through the intermediaries, Hamas. After Mr. Biden’s call, top aides, including the director of the C.I.A., met with the emir in Qatar to go over the latest draft — a six-page text with detailed steps for implementation on both sides.
Within a week, the diplomatic pressure paid off. On Tuesday evening, as the Israeli cabinet took its final vote to approve the deal, Mr. Biden headed out of Washington for a five-day Thanksgiving vacation with his family on the island of Nantucket.
The Israeli decision, announced by Mr. Netanyahu’s office, would allow for a pause of at least four days in the fighting in Gaza. If it holds, it would be the longest halt in hostilities since Hamas’s Oct. 7 attacks prompted Israel to begin its bombardment of Gaza.
But even with the deal in place, Mr. Biden faces challenges ahead. There are still Americans being held hostage in Gaza, and the tensions in the United States, and within his own party, show few signs of diminishing.
Officials said they were keenly aware that the horror for the families of those still in captivity in Gaza will not end until their loved ones are home.
The senior administration official who spoke to reporters Tuesday night said the administration was “determined to get everybody home,” and said the negotiations would continue until that happens.