The special counsel investigating President Biden said in a report released on Thursday that he had decided not to seek prosecution of Mr. Biden over his handling of classified material after leaving the vice presidency in early 2017, but had found evidence that Mr. Biden willfully retained and disclosed some sensitive material.

The report said that 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 internal White House briefings.

Robert K. Hur, the special counsel, said in his report that Mr. Biden had shared the notebooks with a ghostwriter who helped him on his 2017 memoir, “Promise Me, Dad.”

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, said his decision not to pursue criminal charges would have been the same even if Justice Department policy did not preclude indicting a sitting president.

“We conclude that the evidence does not establish Mr. Biden’s guilt beyond a reasonable doubt,” wrote Mr. Hur.

Mr. Hur cited Mr. Biden’s cooperation with investigators, in stark contrast with former President Donald J. Trump’s behavior when documents were discovered at his resort in Florida, as one of the factors in his decision not to bring charges.

While Mr. Hur decided not to prosecute Mr. Biden, his reasons for doing so are likely to raise new questions about the president’s conduct and his mental state.

It will also provide potent new political arguments for Mr. Trump in his battle to discredit the department over its far more serious investigation into his retention of classified materials, which resulted in criminal charges last summer.

In a conversation recorded at a rented property in Virginia in February 2017 — a month after he left office — Mr. Biden told his ghostwriter he had “just found all the classified stuff downstairs.”

Mr. Hur said that exchange was the strongest basis for a prosecution he had found, but that a jury was unlikely to convict Mr. Biden, given the fact that he had grown accustomed to legally retaining documents as vice president, might have not fully adjusted to the new restrictions and believed he had the right to keep them — based on President Reagan’s retention of similar materials.

That the document was discovered in his Delaware garage in a “badly damaged box surrounded by household detritus” indicated he simply may have forgotten he had it over the years, rather than intentionally breaking the law, Mr. Hur concluded.

Another reason he chose not to prosecute Mr. Biden was even less flattering. Mr. Hur cited Mr. Biden’s poor recollection of events during an interview with prosecutors last fall that lasted two days.

“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 after Mr. Biden left office that “a former president well into his eighties” was guilty of a felony that “requires a mental state of willfulness.”