SAN SALVADOR, El Salvador—Attorney General William Barr said his review of the origins of the Russia investigation is focused on U.S. intelligence gathering before the Federal Bureau of Investigation opened its formal inquiry in July 2016 and could lead to rule changes for counterintelligence investigations of political campaigns.

“Government power was used to spy on American citizens,” Mr. Barr told The Wall Street Journal, in his first interview since taking office in February. “I can’t imagine any world where we wouldn’t...