Mr. McCabe’s memo, one of several that he wrote, highlights the conflicting roles that Mr. Rosenstein plays in the case. He supervises the special counsel investigation and has told colleagues that protecting it is among his highest priorities. But many current and former law enforcement officials are suspicious of some of his other actions, including allowing some of Mr. Trump’s congressional allies to view crucial documents from the investigation.

On Thursday night, the New York Times reported that President Trump tried to fire special counsel Robert Mueller last June. Trump ordered White House counsel Donald F. McGahn to oust Mueller, but backed down when McGahn threatened to resign. Trump, however, has publicly denied even considering firing Mueller.