The special counsel investigating President Biden said in a report released on Thursday that he had decided “no criminal charges are warranted” against Mr. Biden over his handling of classified material after leaving the vice presidency in early 2017, but had found evidence that Mr. Biden had willfully retained and disclosed some sensitive material.

Robert K. Hur, the special counsel, said in his highly unflattering report 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.

The report said that Mr. Biden had shared 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.

While Mr. Hur decided not to prosecute Mr. Biden, some of his reasons for doing so are likely to raise new questions about the president’s conduct and his mental state, portraying him as unable in interviews to remember key dates of his own vice presidency — and even precisely when his son Beau had died.