The question yelled at Joe Biden by a reporter was unapologetically blunt: “Who do you think deserves credit for this Mr. President: you or [Donald] Trump?”

Biden had just finished announcing what he presented as his signature foreign policy achievement – a ceasefire-for-hostages deal between Israel and Hamas to halt the bloody war in Gaza that has left 46,000 Palestinians and 1,700 Israelis dead. He wasn’t in the mood for that debate.

“Is that a joke?” the president asked and then walked away flanked by vice-president Kamala Harris and secretary of state Antony Blinken.

Success has many fathers. When the ceasefire in Gaza was finally announced on Thursday, they all stood up to take the credit.

Biden in a press conference said that the ceasefire was “developed and negotiated by my team and will be largely implemented by the incoming administration.” As he praised his diplomats, he grew wistful: “The Bible says blessed are the peacemakers. Many peacemakers helped make this deal happen.”

But there was little public soul-searching about why the plan he had proposed in May – the “exact” same plan as Biden reminded reporters – was finally accepted only days before Donald Trump’s inauguration.

That fact did not escape the attention of president-elect Trump. “This EPIC ceasefire agreement could have only happened as a result of our Historic Victory in November, as it signaled to the entire World that my Administration would seek Peace and negotiate deals to ensure the safety of all Americans, and our Allies,” he said in a post on Truth Social, a social media network.

The truth may lie somewhere in the middle. According to a senior Biden administration official, Trump and Biden’s teams forged an unlikely partnership to secure the complex ceasefire during a transition marked by animosity and distrust.

As the deal was announced on Wednesday, there were even notes of bonhomie between the rival teams, with Biden administration officials praising the partnership between diplomat Brett McGurk and Trump’s envoy to the region, Steve Witkoff.

“It was really quite remarkable,” said the official, who spoke on the condition of anonymity to discuss the negotiations.

Biden had told Trump he wanted to work together to secure a deal when the two met in the Oval Office shortly after Trump’s surprise victory in the November elections, according to the official.

In the final days of the negotiation this month, Witkoff, who does not hold any formal position in government, was invited to travel to Doha alongside the Biden administration officials taking part in negotiations.

In one extraordinary moment, the official said, Witkoff was dispatched on his own to Israel to meet with prime minister Benjamin Netanyahu in a high-stakes gambit to convince him to take the ceasefire deal.

The meeting between Witkoff and Netanyahu, which took place during Shabbat over the initial objections of Netanyahu’s aides, was described as “tense”, according to Israeli media. Reports said that Witkoff put pressure on Netanyahu to accept a ceasefire-for-hostages deal and agree to key concessions to halt the war sooner.

“I thought that was quite effective,” the Biden administration official said.

The Times of Israel, citing its own sources, put it less charitably for the Biden camp: “Arab officials: Trump envoy swayed Netanyahu more in one meeting than Biden did all year.”

In his public statements on the deal, Netanyahu appeared to snub Biden, calling president-elect Trump first to thank him “for his help in advancing the release of the hostages and helping Israel to bring an end to the suffering of dozens of hostages and their families.”

After relaying plans to come to Washington to meet with Trump to discuss the situation around Gaza, he added a curt line about his work with Biden: “prime minister Netanyahu then spoke with US President Joe Biden and thanked him as well for his assistance in advancing the hostages deal.”

Leaked details of the meeting between Netanyahu and Witkoff may have elements of “theater to give Netanyahu cover for finally accepting a deal,” said Matt Duss, the executive vice-president at the Center for International Policy and a former foreign policy adviser to Senator Bernie Sanders “But also, I think the fact is that Netanyahu understands that Trump is coming into office. He’s made clear he wants this war to end, and Trump operates according to a very different calculus than Biden.”

“Biden has always made clear that no matter what Netanyahu does, he will continue to have unconditional, unstinting American support,” he said. “Netanyahu cannot be sure of that with Trump.”

In the US, Biden has faced attacks from both the right and left on his handling of the war, as well as anger among officials who believed that the United States was not putting sufficient pressure on Israel to halt its campaign in Gaza.

Dozens of officials at the state department have bristled in public and private at the administration’s handling of the war, arguing that Biden and his aides’ refusal to threaten to halt deliveries of arms and other aid to Israel over the war may have prolonged the military campaign.

A Pentagon official previously told the Guardian that the ceasefire was “being driven by Trump’s team … and Biden, Blinken and the whole administration secured its legacy as enablers.”

Pro-Trump Republicans have been equally scathing about Biden’s efforts to end the war, although they have targeted him as too soft on Hamas.

Senator John Cornyn of Texas on Thursday said that the deal was “encouraging but obviously we know that President Biden has not been the best negotiator when it comes to these deals.”

Trump had previously warned that “all hell will break out in the Middle East” if a deal was not reached before his inauguration.

Asked whether those threats may have led to the ceasefire, Cornyn replied: “I don’t believe in coincidences. So I do believe that President Trump had an impact on this deal. And obviously the Biden administration is eager to wrap this up.”

Yet the sharpest anger against Biden over the war has been voiced by progressives, who have said that the administration’s overwhelming support for Israel may have both prolonged the war and cost the Harris campaign crucial votes on the left in the November elections.

The ceasefire had come too late, some said, and would do little to burnish Biden’s legacy on foreign policy.

“No one’s going to buy that Biden delivered this ceasefire. No one,” said Duss. “He continued to give Netanyahu political cover, even as Netanyahu repeatedly undermined the possibility of a ceasefire.”