Key Democrats are questioning the memo Deputy Attorney General Rod Rosenstein wrote justifying the ouster of FBI Director James B. Comey, saying it doesn’t sound like the kind of document someone with the lawyer’s long experience would craft — and saying it’s more evidence for why he should recuse himself from probing President Trump.

The questions come as The Washington Post reported Mr. Rosenstein was so unsettled by the way the White House portrayed his role in the firing that the No. 2 man at the Justice Department had threatened to resign.

Justice Department spokeswoman Sarah Isgur Flores said the report that Mr. Rosenstein threatened to quit was false.

In his May 9 memo, Mr. Rosenstein says Mr. Comey “made serious mistakes” in his public handling of the investigation into former Secretary of State Hillary Clinton’s secret emails, and was unable to regain the trust of the public.

Mr. Rosenstein cited the criticism from former top Justice Department officials in both Democratic and Republican administrations as proof that Mr. Comey had goofed, and had hurt the reputation of the bureau.

But Sen. Dianne Feinstein, the top Democrat on the Senate Judiciary Committee, said the memo didn’t sound right.

“Instead of a document that provides meaningful analysis, the memo reads like political document,” she said. “It includes quotes from op-eds and television appearances that are as old as six months. It doesn’t include any contemporary insights from inside the FBI. The memo appears to have been hastily assembled to justify a preordained outcome.”

Just weeks ago, Democrats had insisted Mr. Rosenstein be put in charge of overseeing the FBI’s investigation into Trump campaign figures’ ties with Russia, but now they say the memo disqualifies Mr. Rosenstein. They have demanded that the oversight to appoint a special prosecutor be given instead to the top career attorney at the department.

The White House has said Mr. Rosenstein and Attorney General Jeff Sessions brought their concerns to Mr. Trump, who then told them to put the matters in writing. Memos from both of the men were used to justify Mr. Trump’s decision to fire Mr. Comey.

• Andrea Noble contributed to this article.

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