When President Biden appeared at a last-minute news conference on Thursday night, he hoped to assure the country of his mental acuity hours after a special counsel’s report had devastatingly referred to him as a “well-meaning, elderly man with a poor memory.”

Instead, a visibly angry Mr. Biden made the exact type of verbal flub that has kept Democrats so nervous for months, mistakenly referring to the president of Egypt, Abdel Fattah el-Sisi, as the “president of Mexico” as he tried to address the latest developments in the war in Gaza.

The special counsel’s report and the president’s evening performance placed Mr. Biden’s advanced age, the singularly uncomfortable subject looming over his re-election bid, back at the center of America’s political conversation.

The 81-year-old president — already the oldest in the nation’s history — has for years fought the perception that he is a diminished figure. “My memory is fine,” he insisted on Thursday from the White House.

Yet in a single cutting phrase, the report from Robert K. Hur, the special counsel who had investigated Mr. Biden’s handling of classified documents, captured the fears of Democrats who hold their breath when Mr. Biden appears in public and the hopes of Republicans, especially former President Donald J. Trump and his allies. The Trump operation has made plain its intent to use Mr. Biden’s stiffer gait and sometimes garbled speech to cast him as weak.

The Biden campaign has built its strategy around telling voters that the November election is a choice between the president, whatever doubts the public has about his age, and an opponent in Mr. Trump, 77, whom they paint as a threat to democracy and personal freedoms.

Democrats long ago cast their lot with Mr. Biden. With no serious alternative in the primary race, many in the party believe the country’s future is riding on the president’s ability to persuade voters that he is still up for the job for another four years.

But for all of Mr. Trump’s vulnerabilities — the Republican Party has been on a protracted losing streak since he rose to power — the upward of $2 billion that the Biden campaign and its allies hope to raise and spend will not make the current president any younger.

And Thursday night’s news conference was an example of the political dangers for Mr. Biden, whose missteps are magnified in part by the White House team’s tight control over his media exposure. His aides are so risk averse that they passed even on a pre-Super Bowl interview this weekend before one of the nation’s largest annual television audiences.

“Fair or not, you can’t unring the bell,” said David Axelrod, the former strategist for Barack Obama who has emerged as one of the Democratic Party’s leading figures warning about how voters view Mr. Biden’s age. Mr. Axelrod said the special counsel’s report was so troubling for Democrats because it “goes to the core of what is plaguing Biden politically now, which is a widespread fear that he’s not up to it.”

He added: “The most damaging things in politics are the things that confirm people’s pre-existing suspicions, and those are the things that travel very fast. It’s a problem.”

The Biden campaign declined to comment.

As a legal matter, Mr. Hur’s report absolved Mr. Biden of criminal wrongdoing, announcing that there was insufficient evidence to charge him. But Democrats seized on his loaded language — Mr. Hur also invoked Mr. Biden’s “diminished faculties in advancing age” as something that would have been sympathetic to a jury — to accuse the special counsel, who was once a Trump appointee, of partisan motives.

For Republicans aiming to oust Mr. Biden, the report and the president’s angry response came as a gift after several days in which their own dysfunction in Congress dominated the news. The Republican National Committee quickly created a graphic with the report’s eight most brutal words — “well-meaning, elderly man with a poor memory” — grafted onto the Biden campaign logo.

Never mind that the special counsel declined to charge Mr. Biden while Mr. Trump’s own, more serious case over whether he mishandled classified documents remains part of the 91 felony charges he faces across four jurisdictions.

Still, Chris LaCivita, a top strategist for Mr. Trump, called the special counsel’s description of Mr. Biden “damning and defining.”

“The report confirms what Americans have been witnessing across their TV screens for the last few years — that an elderly man with a poor memory is leading America into a morass of wars, inflationary disaster and lack of opportunity for taxpaying Americans,” Mr. LaCivita said.

Senator Chris Coons, a Delaware Democrat who is close to Mr. Biden, predicted that he would receive more calls from “people expressing concern.” But he said he would respond by recounting his direct experiences with Mr. Biden, which he said demonstrated that the president was “sharp, engaged and purposeful.”

Still, Mr. Biden’s mix-up of Egypt and Mexico came soon after a couple of slips in the last week regarding deceased European leaders. First, during a campaign swing in Nevada, he confused François Mitterrand, a former French president who died in 1996, with the country’s current president, Emmanuel Macron. Then, on Wednesday, he referred twice to having met in 2021 with Helmut Kohl, a former German chancellor who died in 2017, instead of with Angela Merkel, who led the country three years ago.

Mr. Coons made light of “the calls I get from freaked-out Democrats saying, ‘Oh my God, the president said X!’ I think, ‘And the former president said Y!’ If you asked Donald Trump who François Mitterrand was, he would look at you like, ‘What are you talking about?’”

Mr. Trump has made his own series of verbal stumbles — he recently confused Nikki Haley with Nancy Pelosi and previously mixed up the leaders of Hungary and Turkey — but polls show that voters do not question his sharpness the same way they do Mr. Biden’s. An NBC News poll released this week found that voters gave Mr. Trump an advantage of 16 percentage points on the question of who was more competent and effective — a 25-point swing since 2020, when Mr. Biden held a nine-point edge on that question.

Ms. Haley has argued that a new generation would better serve the country and both parties. “The first party to retire its 80-year-old candidate is going to win this election!” she wrote in a fund-raising email on Thursday.

Mr. Biden’s aides stressed privately that suggestions that his memory is lapsing would not hurt him because voters have already priced in his age when considering whether to support him against Mr. Trump. Some of the president’s allies on Thursday dusted off a playbook used by past presidents facing inquiries: Attack the investigators as motivated by partisan politics.

Representative Robert Garcia, a California Democrat, said Mr. Hur had no expertise to judge Mr. Biden’s memory.

“The folks writing this report, they are lawyers, they’re not doctors,” Mr. Garcia said. “This person’s a Republican who couldn’t find any evidence. He’s probably trying to hurt the president politically.”

For many Democrats, the episode was an unwelcome echo of the approach to the 2016 election. James B. Comey, the F.B.I. director at the time, held a news conference that summer to declare that he would not charge Hillary Clinton over her use of a private email server, but he still excoriated her judgment — and then, months later, reopened his investigation in the days before the election.

“This, for many of us, brings back the 11 days prior to Clinton-Trump,” said Bakari Sellers, a Democratic strategist, who predicted that Mr. Biden’s troubles would blow over because the election remains far away. “The blessing for Biden is that he was old before this report, he’ll be old after this report. We all knew he is old.”

The special counsel’s report was surprisingly blunt. It described Mr. Biden’s memory as appearing to have “significant limitations,” characterized an interview he recorded in 2017 as “painfully slow” and said Mr. Biden did not remember some key dates of his vice presidency or “when his son Beau died.”

In a letter to the special counsel, Mr. Biden’s lawyers called the numerous references to Mr. Biden’s memory “gratuitous,” as well as “prejudicial and inflammatory.” And Mr. Biden himself, with visible frustration, expressed disbelief at the idea he did not know when his son had died: “How in the hell dare he raise that?”

Representative Daniel S. Goldman, a New York Democrat and a former federal prosecutor, said the attention that Mr. Biden’s Mexico-Egypt slip instantly attracted was a “perfect example of where the age issues get completely exaggerated and blown out of proportion.”

Mr. Biden remains almost certain to be the Democratic nominee. He has won his party’s first nominating contests with ease, and deadlines to qualify for the Democratic primary ballot have passed in about 80 percent of states and territories.

Representative Dean Phillips of Minnesota, who is Mr. Biden’s only remaining Democratic primary challenger, has attracted little support so far. Mr. Phillips said the special counsel’s description of Mr. Biden’s memory showed that “the president is not in a position to continue to serve as our commander in chief beyond January 2025.”

James Carville, the veteran Democratic strategist, said that the negative perceptions of Mr. Biden’s age could not be dismissed as a distraction.

“The public does not view his age as — that’s not a Fox News issue,” he said in an interview after the news conference. “It’s not a Taylor Swift rigging the Super Bowl kind of thing. So — I don’t know how you get out of this.”

“The whole day,” he added, “was confirming an existing suspicion.”

Maggie Haberman contributed reporting.