Paul Clarke, 71, from East Sussex but now living in Manchester, entered the pleas at Lewes Crown Court.
He had been charged with possessing an indecent image of a child, possession of prohibited images and making a total of 3,100 indecent images of children.
He is due to be sentenced on 5 February.
Clarke, of Redclyffe Road, Urmston, Greater Manchester, but formerly of Watchbell Road, Rye in East Sussex, was arrested after a search of his Rye address - the residential presbytery attached to St Anthony's Church - in November 2014.
Police said the charges all related to images taken from the internet.
A Roman Catholic priest has pleaded guilty to five charges in connection with more than 3,000 indecent images of children.