On 10 December 1988, Pope John Paul II appointed him titular archbishop of Otriculum and Apostolic Nuncio to Bangladesh. He received his episcopal consecration from the Secretary of State Cardinal Agostino Casaroli on 25 February 1989. Biggio was apostolic nuncio in Chile from 1992 to 1999. In that role he advised against prosecuting former Chilean dictator Augusto Pinochet for crimes against humanity, suggesting he be given diplomatic immunity, pardoned and prayed for. He called Pinochet's arrest by British authorities on a Spanish warrant a "violation of diplomatic immunity".