WASHINGTON — The Justice Department’s inspector general said Thursday that he would open a broad investigation into how the F.B.I. director, James B. Comey, handled the case over Hillary Clinton’s emails, including his decision to discuss it at a news conference and to disclose 11 days before the election that he had new information that could lead him to reopen it.

The inspector general, Michael E. Horowitz, will not look into the decision not to prosecute Mrs. Clinton or her aides. But he will review actions Mr. Comey took that Mrs. Clinton and many of her supporters believe cost her the election.

They are: the news conference in July at which he announced he was not indicting Mrs. Clinton but described her behavior as “extremely careless”; the letter to Congress in late October in which he said that newly discovered emails could potentially change the outcome of the F.B.I.’s investigation; and the letter three days before the election in which he said that he was closing it again.

The inspector general’s office said that it was initiating the investigation in response to complaints from members of Congress and the public about actions by the F.B.I. and the Justice Department during the campaign that could be seen as politically motivated.