WASHINGTON — Attorney General William P. Barr has assigned the top federal prosecutor in Connecticut to examine the origins of the Russia investigation, according to two people familiar with the matter, a move that President Trump has long called for but that could anger law enforcement officials who insist that scrutiny of the Trump campaign was lawful.

John H. Durham, the United States attorney in Connecticut, has a history of serving as a special prosecutor investigating potential wrongdoing among national security officials, including the F.B.I.’s ties to a crime boss in Boston and accusations of C.I.A. abuses of detainees.

His inquiry is the third known investigation focused on the opening of an F.B.I. counterintelligence investigation during the 2016 presidential campaign into possible ties between Russia’s election interference and Trump associates.

The department’s inspector general, Michael E. Horowitz, is separately examining investigators’ use of wiretap applications and informants and whether any political bias against Mr. Trump influenced investigative decisions. And John W. Huber, the United States attorney in Utah, has been reviewing aspects of the Russia investigation. His findings have not been announced.