Mr. Trump’s verbal assaults have put Mr. Wray and his leadership team in a difficult position. Mr. Wray is trying to move past his predecessor’s era and make sure there is not a whiff of politics at the F.B.I. He has promised the F.B.I.’s work would be based on the “facts, the law and the impartial pursuit of justice — period.”

Yet Mr. Trump and his allies in Congress are making that task much harder.

Current and former F.B.I. officials say Mr. Trump’s criticisms, and those of normally supportive Republican members of Congress, have damaged morale in some quarters of the bureau. Senior agents have expressed fear that if their names appear in the news media, they will be singled out for attack by politicians.