 In the interval between the death of Viceroy Diego de Benavides, 8th Count of Santisteban in 1666 and the arrival of his replacement, Pedro Antonio Fernández de Castro, the following year, Iturriaza served as governor (interim viceroy) of Peru.This was from about March 1666 to about November 1667.He served again from about December 1672 to about August 1674, between the death of Fernández de Castro and the arrival of Baltasar de la Cueva Enríquez.