The White House quickly backed off the president’s remarks and said Mr. Obama was not trying to influence the investigation. But his comments spread quickly, raising the ire of officials who saw an instance of the president trying to influence the outcome of a continuing investigation — and not for the first time.

A spokesman for the F.B.I. declined to comment. But Ron Hosko, a former senior F.B.I. official who retired in 2014 and is now the president of the Law Enforcement Legal Defense Fund, said it was inappropriate for the president to “suggest what side of the investigation he is on” when the F.B.I. is still investigating.

“Injecting politics into what is supposed to be a fact-finding inquiry leaves a foul taste in the F.B.I.’s mouth and makes them fear that no matter what they find, the Justice Department will take the president’s signal and not bring a case,” said Mr. Hosko, who maintains close contact with current agents.