The long-sought and painstakingly negotiated Gaza ceasefire agreement announced Wednesday came about in part through a remarkable collaboration between President Biden and President-elect Donald J. Trump, who temporarily put aside mutual hostilities to achieve a common goal.

The two presidents directed their advisers to work together to get Israel and Hamas across the finish line to reach an agreement to end the fighting that has ravaged Gaza and release hostages held there for 15 months. The deal is scheduled to begin on Sunday, a day before Mr Biden hands over the White House to Mr Trump.

Each president had his own interest in settling the matter before Inauguration Day. For Mr. Biden, the deal, if passed, represents a final vindication of his term in office. He hopes it will end the deadliest war in the history of the Israeli-Palestinian conflict while freeing both Americans and Israelis from captivity . For Mr. Trump, the deal takes a major issue off the table for now, opening up a second term and giving him the freedom to pursue other priorities.

The dramatic development, just five days before the transfer of power in the United States, went against the grain in Washington, where presidents from opposing parties rarely work together during a transition, even in the face of a major crisis. But the political planets quickly returned to their normal orbits as both sides argued over who deserved credit for resolving the standoff.

While Mr. Biden waited for official word to come from the region, Mr. Trump beat him to it by revealing the deal himself in all caps in a social media post. “This EPIC ceasefire agreement could only come about as a result of our historic victory in November,” he added shortly afterwards.

When Mr. Biden appeared before the cameras at the White House later that afternoon, he appeared friendlier, noting that the two teams spoke with one voice. But he bristled when asked who deserved credit, him or Mr. Trump. “Is this a joke?” he asked.

Still, the partnership, delicate and delicate as it was, stood out at a time of deep polarization. “It’s really extraordinary,” said Mara Rudman, who was deputy special envoy for Middle East peace under President Barack Obama. “Everyone talks about who gets credit, but the fact is it’s shared, and one of the reasons it worked is because it’s shared.”

That does not mean that it would lead to lasting synergies on this or other issues. “This was a case where doing the right thing also aligned with the best political interests of the people,” said Ms. Rudman, now a researcher at the University of Virginia’s Miller Center.

However the credit is ultimately distributed, diplomats, officials and analysts said it seemed clear that both presidents played important roles. The deal finally agreed upon was essentially the same one that Mr. Biden had put on the table last May and which his envoys, led by Brett H. McGurk, his Middle East coordinator, had laboriously worked to make acceptable to both sides make.

At the same time, Mr. Trump’s impending return to power and his blustery threat that “all hell will break loose” if the hostages are not released by his swearing-in have significantly altered the warring parties’ calculations. Israeli Prime Minister Benjamin Netanyahu, who received so much support from Mr. Trump in his first term, could not assume that the new president would support him if he prolonged the war during his second term.

In fact, it was telling that after the deal was announced, Mr. Netanyahu, who goes by the nickname Bibi, first called Mr. Trump to thank him and only then called Mr. Biden. In a statement, Mr. Netanyahu stressed his gratitude to Mr. Trump “for his comments that the United States will work with Israel to ensure that Gaza never becomes a haven for terrorists.” Mr. Biden was only mentioned in the fourth paragraph and only in a single sentence in which he “also” thanked him for his help.

Mr. Trump’s desire to force a deal went beyond his typical public threats and also extended to constructive support on the ground. He authorized Steve Witkoff, his longtime friend whom he appointed special envoy to the Middle East, to work with Mr. McGurk to push negotiators to finalize the deal. Mr. McGurk and his team welcomed the help and used Mr. Witkoff’s support as leverage.

“That was Biden’s deal,” former Rep. Tom Malinowski, Democrat of New Jersey, wrote on social media, “but as much as I hate to say it, he couldn’t have done it without Trump — not so much because of Trump performative threats.” Hamas, but his willingness to bluntly tell Bibi that the war must end by January 20.”

There were some Republicans willing to praise Mr. Biden for his efforts to forge the deal with Mr. Trump. “It’s good to see the Biden Administration and Trump Transition working together to get this deal done,” Sen. Thom Tillis of North Carolina wrote on social media.

Few transitions have experienced such a moment of overlapping interests. In the midst of the Great Depression, defeated President Herbert Hoover tried to persuade President-elect Franklin D. Roosevelt to come together to deal with a banking crisis, but was rebuffed by a new leader who did not want to be tied to his predecessor.

A more sinister example came 44 years ago, when President Jimmy Carter worked until the final hours of his presidency to free 52 American hostages held in Iran, without the help of his successor, President-elect Ronald Reagan. In fact, some evidence has emerged suggesting that people around Mr. Reagan tried to stop Iran from releasing the hostages before the election out of fear that it would help Mr. Carter, although official investigations have never confirmed this.

Mr. Carter eventually struck a deal to release the hostages, but in a final insult, Iran held back the planes with the Americans on board until Mr. Reagan was sworn in on January 20, 1981. This memory was not lost on Mr. Carter. Biden’s team in recent weeks, particularly after Mr. Carter’s death last month. Government officials and their allies had spent the past few days morbidly pondering the possibility that history could repeat itself.

The impending change in political leadership in the United States was not the only factor driving negotiations over the war in Gaza. The situation on the ground has changed dramatically since Mr. Biden first offered his ceasefire proposal in May.

Meanwhile, Israel has beheaded Hamas’ leadership, nearly destroyed its allied militia Hezbollah in Lebanon and destroyed key military facilities in Iran. A Biden-brokered ceasefire in Lebanon left Hamas without a second front against Israel and further isolated it. And the overthrow of President Bashar al-Assad in Syria only reinforced the weakness of Iran and its allies and proxies.

But the approaching Inauguration Day in Washington presented a new, action-intensive deadline that was hard to ignore. Mr. Trump said little about the war during the campaign, but when he did, he made clear he was not happy about it and called on Israel to end the war as quickly as possible because of the heartbreaking images of death and destruction performances in Gaza damaged Israel’s reputation on the international stage.

Moreover, Mr. Trump’s relationship with Mr. Netanyahu has evolved since his first term, when he presented himself as the Israeli leader’s most loyal ally. Mr. Trump cut aid to the Palestinians, moved the U.S. embassy to Jerusalem, recognized Israeli authority over the Golan Heights and directed diplomatic openings between Israel and several of its Arab neighbors.

But their relations deteriorated in Mr. Trump’s final year in office when he felt Mr. Netanyahu was taking advantage of him, and they deteriorated even more when the prime minister congratulated Mr. Biden on a victory in the 2020 election that Mr. Trump still holds denies. Mr. Netanyahu has worked diligently in recent months to reconcile with Mr. Trump.

As for Mr. Biden, his own relationship with Mr. Netanyahu has been strained since the days shortly after the Hamas-led terrorist attack on Oct. 7, 2023, when he flew to Israel and hugged the Israeli leader on the tarmac. Biden advisers and allies have suggested that Mr. Netanyahu deliberately withheld a ceasefire deal to let Mr. Trump win, in an attempt to kowtow to him.

Mr. Biden said nothing about it during his televised address on Wednesday. But after 15 months of trying to manage the Middle East crisis and avert a larger regional war, he seemed relieved that an end was at hand.

“I am deeply pleased that this day has finally come, for the good of the people of Israel and the families who wait in agony, and for the good of the innocent people of Gaza who have suffered unimaginable devastation caused by the war,” Mr. Biden said .

He referred to working with Mr. Trump without mentioning him by name. “I would also like to note that this deal was developed and negotiated under my administration,” Mr. Biden said, flanked by Vice President Kamala Harris and Secretary of State Antony J. Blinken. “But its terms will largely be implemented by the next government. In the last few days we have spoken as a team.”

Asked about Mr. Trump’s role, Mr. Biden noted that the ceasefire was “the exact framework of the agreement that I proposed back in May,” and claimed to have given Israel the support it needed to defeat Hamas, Hezbollah and Iran weaken. “I knew this deal had to be implemented by the next team,” he added, “so I told my team to coordinate closely with the new team to make sure we all spoke with the same voice because that is what American presidents do.”

Mr. Trump made no mention of the role of his predecessor’s team, leaving the impression in his social media posts that he reached the agreement alone.

“We have accomplished so much without even being in the White House,” he wrote. “Imagine all the wonderful things that will happen when I return to the White House and my administration is fully confirmed so they can secure further victories for the United States!”