Corradi, 82, and another priest, 55-year-old Horacio Corbacho, were arrested last month along with three employees for the alleged abuse of at least 24 deaf children who attended the Antonio Provolo Institute, in the city of Mendoza.
Police raided the institute and found magazines featuring naked women and about $34,000 in Corradi's room.
They allege nothing was done then nor later in 2014, when they told Pope Francis in a letter that Corradi was living in his native Argentina.
All five suspects in the Mendoza case are being held in jail and have not spoken publicly since their arrest.
"From the pope down ... all of the Catholic Church hierarchy is the same. They all knew," one of the victims told The Associated Press through a sign language interpreter.
Another victim said the priests would rape again if released.
"This happened in Italy ... it happened again here, and it must end," the victim said, insisting on speaking anonymously. "Enough!"
Victims and prosecutors say the anal and vaginal rapes, fondling and oral sex by the priests took place in the bathrooms, dorms, garden and a basement at the school in Lujan de Cuyo, a city about 620 miles northwest of Buenos Aires.
The school has "a little chapel with an image of the Virgin and some chairs where the kids would get confession and receive the communion. That's where some of the acts were happening," Fabrizio Sidoti, the prosecutor who has been leading the investigation since the scandal broke, told the AP.
Children from other regions of Argentina who lived at the dorms were especially vulnerable and often targeted by the abusers. The tales are harrowing: One of the victims told the AP she witnessed how a girl was raped by one priest while the other one forced her to give him oral sex.
The prosecutor is expecting more than 20 other people to provide testimony and more victims to come forward.
Pope Francis has not spoken publicly about the case and the Vatican declined to comment.
Advocates of sex abuse victims by priests question how Francis could have been unaware of Corradi's misdeeds, given he was publicly named by the Italy victims.
"No other pope has spoken as passionately about the evil of child sex abuse as Francis. No other pope has invoked 'zero tolerance' as often. No other pope has promised accountability of church superiors," said Anne Barrett Doyle, co-director of BishopAccountability, an online resource about clerical abuse. "In light of the crimes against the helpless children in Mendoza, the Pope's assurances seem empty indeed."
On Dec. 11, the pope appeared in a video using sign language to wish deaf people worldwide a merry Christmas — a gesture that fell particularly flat in Argentina as Catholics struggle with the enormity of the scandal.
"Either he lives outside of reality or this is enormously cynical ... it's a mockery," said Carlos Lombardi, an attorney who specializes in canon law.