Each president had a vested interest in getting the matter resolved before inauguration day. For Mr. Biden, the deal, if it goes ahead, represents the final vindication on his watch, which he hopes will end the deadliest war in the history of the Israeli-Palestinian conflict with the release of Americans as well as Israelis from captivity. For Mr. Trump, the deal takes one major issue off the table for now as he opens a second term, freeing him to pursue other priorities.

The dramatic development, just five days before the transfer of power in the United States, struck a chord in Washington, where presidents of opposing parties rarely work in tandem 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 impasse.

While Mr. Biden waited for official word from the region, Mr. Trump jumped him by revealing the deal himself in a social media post in all caps. “This EPIC ceasefire agreement could only have happened as a result of our historic victory in November,” he added soon after.

When Mr. Biden appeared on camera at the White House later in the afternoon, he was more gracious, noting that the two teams spoke with one voice. But he bristled when asked who was to blame, him or Mr. Trump. “Is that a joke?” he asked.

Still, the partnership, however awkward and tricky, stood out in an era of deep polarization. “It’s really remarkable,” said Mara Rudman, who was deputy special envoy for Middle East peace under President Barack Obama. “Everybody talks about who gets credit, but the fact is credit is shared and part of the reason it worked is because it was shared.”

This did not mean that it would lead to lasting synergy on this or other issues. “This was a case where the right thing to do was aligned with the best political interest of the people,” said Ms. Rudman, now a research fellow at the University of Virginia’s Miller Center.

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

At the same time, Mr. Trump’s imminent return to power and his crass threat to “break all hell out” if the hostages are not released by the time he is sworn in have apparently changed the warring parties’ calculations. Israeli Prime Minister Benjamin Netanyahu, the beneficiary of so much support from Mr. Trump during his first term, he could not take for granted that the new president would support him if he extended the war during his second term.

Indeed, it was significant that Mr. Netanyahu, who goes by the nickname Bibi, first called Mr. Trump to thank him after announcing the agreement, and only then Mr. Biden. In a statement, Mr. Netanyahu emphasized his gratitude to Mr. Trump “on his remarks that the United States will work with Israel to ensure that Gaza will never be a haven for terrorists.” Mr. Biden is not mentioned until the fourth paragraph and only in one sentence in which “he too” is thanked for his help.

Mr. Trump’s desire to force a deal went beyond his well-known public threats and extended to constructive assistance on the ground. He authorized Steve Witkoff, his longtime friend whom he had chosen as special envoy for the Middle East, to to work with Mr. McGurk put pressure on the negotiators to finalize the agreement. Mr. McGurk and his team were happy to have the help and support of Mr. Witkoff as an advantage.

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

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

Few transitions have seen such a moment of intersecting interests. In the midst of the Great Depression, defeated President Herbert Hoover tried to enlist President-elect Franklin D. Roosevelt to join forces in solving the banking crisis, only to be rebuffed by the incoming leader who did not want to be tied to his predecessor.

And more an eerily haunting example it 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 to suggest that people around Mr. Reagan tried discourage Iran from releasing the hostages before the election for fear it would help Mr Carter, although official investigations have never confirmed this.

Mr. Carter eventually struck a deal to free the hostages, but in a final affront, Iran held the planes carrying the Americans until moments after Mr. Reagan sworn in on January 20, 1981. That memory is not lost on Mr. Biden’s team in recent weeks, especially after Mr. Carter’s death last month. In recent days, administration officials and their allies have been thinking morbidly about the possibility of history repeating itself.

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

Meanwhile, Israel has decapitated the leadership of Hamas, nearly destroyed its allied militia Hezbollah in Lebanon, and seized key military facilities in Iran. With Biden’s mediation ceasefire in Lebanon left Hamas without another front against Israel, further isolating it. and the fall of President Bashar al-Assad in Syria has only reinforced the weakness of Iran and its allies and proxies.

But the upcoming Inauguration Day in Washington created a new deadline for action that was hard to ignore. Mr. Trump spoke little about the war during the campaign, but when he did, he made it clear that he was not happy about it and called on Israel to end it as soon as possible because the heartbreaking images of death and destruction in Gaza were damaging Israel’s image on international scene.

Moreover, Mr. Trump’s relationship with Mr. Netanyahu has evolved since his first term, when he presented himself as the Israeli leader’s staunchest ally. Mr. Trump reduce aid Palestinians, moved the US Embassy to Jerusalem, recognized Israeli rule across the Golan Heights and presided diplomatic openings between Israel and several of its Arab neighbors.

But their relationship soured in the last year of Mr. Trump in office when he noticed that Mr. Netanyahu is taking advantage, and they worsened even more when the prime minister congratulated Mr. Biden on winning the 2020 elections, what Mr. Trump is still in denial. Mr. Netanyahu has been hard at work in recent months make peace with Mr. Trump.

What Mr. As for Biden, his own relationship with Mr. Netanyahu has been tense since the day shortly after the terrorist attack led by Hamas on October 7, 2023, when flew to Israel and hugged the Israeli leader on the asphalt. Mr. Biden’s advisers and allies suspected that Mr. Netanyahu was deliberately delaying the cease-fire agreement to hand the victory to Mr. Trump in an effort to curry favor with him.

Mr. Biden said nothing about it during his televised address on Wednesday. But after 15 months of trying to manage the crisis in the Middle East and prevent a wider regional war, he seemed relieved to see it end.

“I am deeply pleased that this day has come, it has finally come, for the sake of the people of Israel and the families who are waiting in agony and for the sake of the innocent people of Gaza who have suffered unimaginable destruction because of the war,” Mr. Biden said.

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

Asked about the role of Mr. Trump, Mr. Biden noted that the cease-fire was “the exact framework of the deal I proposed back in May” and credited it with giving Israel the support it needed to weaken Hamas, Hezbollah and Iran. “I knew this deal would have to be implemented by the next team,” he added, “so I told my team to coordinate closely with the incoming team to make sure we were all speaking with one voice because that’s what American presidents do.”

Mr Trump did not mention the role of his predecessor’s team and gave the impression in his social media posts that he had delivered the deal himself.

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