President Biden angrily hit back against a special counsel’s report on his handling of classified documents on Thursday, denying that he willfully retained papers that he was not entitled to keep and insisting that “my memory is fine” despite questions raised by the prosecutors.

In a hurriedly arranged nighttime televised appearance at the White House, a defiant Mr. Biden offered a feisty defense of his actions and his capacity to run the country, an effort to quell concerns that could hurt his chances for re-election at a time when polls show most voters already think he is too old. The report called him a “well-meaning, elderly man with a poor memory,” a line that clearly got under the president’s skin.

“I’m well meaning, and I’m an elderly man, and I know what the hell I’m doing,” Mr. Biden told a Fox News reporter who asked him about the report after his statement. “My memory is so bad I let you speak.”

Mr. Biden was especially irked that the special counsel indicated that the president could not remember the year his elder son, Beau, died of cancer, a particularly sensitive subject for him. “How in the hell dare he raise that?” Mr. Biden said, sounding emotional.

But even as he sought to dispel suggestions that he might not be up for the job, he confused the presidents of Mexico and Egypt in response to a question about negotiations to release hostages held by Hamas, making exactly the kind of mistake that his staff presumably hoped he would avoid at a time when his mental acuity is being questioned.

“I’m of the view, as you know, that the conduct of the response in Gaza, in the Gaza Strip, has been over the top,” Mr. Biden said. “I think that as you know, initially, the president of Mexico, el-Sisi, did not want to open up the gate to allow humanitarian material to get in.” He evidently was referring to Abdel Fattah el-Sisi, the president of Egypt, not Mexico.

The remarks from the Diplomatic Reception Room at the White House came just hours after the special counsel, Robert K. Hur, cleared him of criminal charges in the handling of classified documents but sharply criticized his conduct and suggested that one reason he could not be prosecuted was because of his memory lapses.

In an unflattering 300-plus-page report, Mr. Hur said Mr. Biden had left the White House after his vice presidency with classified documents about Afghanistan and notebooks with handwritten entries “implicating sensitive intelligence sources and methods” taken from White House briefings. Mr. Hur criticized Mr. Biden for sharing the content of the notebooks with a ghostwriter who helped him on his 2017 memoir, “Promise Me, Dad,” even though he knew some of it was classified.

But the evidence “does not establish Mr. Biden’s guilt beyond a reasonable doubt,” said Mr. Hur, a former Trump Justice Department official appointed by Attorney General Merrick B. Garland in January 2023 to lead the inquiry after classified files were found in the garage and living areas of Mr. Biden’s home in Delaware and his former office in Washington.

The president and his team welcomed the decision not to lodge criminal charges, but were clearly worried that the report’s description of Mr. Biden’s mental capacity could be damaging. At 81, Mr. Biden is already the oldest president in American history and would be 86 at the end of a second term.

Former President Donald J. Trump, who is 77 and has inspired questions about his own cognitive health by making confusing statements at public rallies, has been charged with 40 felonies for taking classified documents with him when he left the White House and attempting to hide them from government officials who tried to retrieve them. He complained bitterly on Thursday that Mr. Biden was not charged.

“I did nothing wrong, and I cooperated far more,” Mr. Trump wrote on social media, not mentioning his refusal to turn over documents that had been subpoenaed and other efforts to thwart investigators. “What Biden did is outrageously criminal.”

In recounting his interviews with the president, Mr. Hur portrayed him as unable to remember key dates of his time in President Barack Obama’s White House. “Mr. Biden would likely present himself to a jury, as he did during our interview with him, as a sympathetic, well-meaning, elderly man with a poor memory,” Mr. Hur wrote. It would be difficult to convince a jury that “a former president well into his 80s” was guilty of a felony that “requires a mental state of willfulness,” Mr. Hur added.

Mr. Biden used his nighttime appearance to respond directly to the report. He said Mr. Hur’s conclusion that he “willfully” retained documents was “misleading” and “just plain wrong” and denied that he had shared classified information with his ghostwriter. He said a memo he wrote to Mr. Obama on Afghanistan that he shared should have been considered simply “private.”

He said his retention of documents was not comparable to Mr. Trump’s behavior. “It wasn’t out in like in Mar-a-Lago, in a public place,” he said, referring to Mr. Trump’s Florida estate and private club. And he blamed his staff for any mistakes in handling classified documents, saying, “I take responsibility for not having seen exactly what my staff was doing.”

But more than anything, Mr. Biden bristled at questions about his age. “That is your judgment,” he snapped at one reporter. Asked why he should not step aside for a younger successor, Mr. Biden said that he was the most qualified person in the country to be president and that he should “finish the job that I started.”