Police arrested Fr Nicola Corradi, 82, Fr Horacio Corbacho, 55, and three other men last week.
They are accused of sexual and physical child abuse at the Antonio Provolo Institute in north-western Mendoza province.
Authorities say the alleged victims are now in their 20s.
The accused have been assigned a public defender and are being held at a jail in Mendoza.
They have not spoken publicly since their arrest.
Fr Corradi earlier had been accused in Italy of sexually abusing students at the Provolo Institute in Verona, a notorious school for the deaf where hundreds of children are believed to have been sexually assaulted over the years by two dozen priests and religious brothers.
Advocates for clerical sex abuse have expressed anger that he wasn’t sanctioned by the Vatican and allegedly went on to abuse children in Argentina.
In a statement to the Associated Press after Fr Corradi’s arrest, the association said they had flagged the priest by name to the Verona archdiocese during hearings held between December 2010 and February 2011.
Fr Corradi’s name was also on a list of accused priests that the association published when the allegations were first aired. His location in Argentina was also listed.
Members of the Provolo association met with the Pope last year and asked for an independent commission to investigate.
The Provolo group provided the AP with the letter from the Vatican dated February 5, 2016, in which the Vatican said it had forwarded the request to the Italian bishops’ conference, saying it was up to them to investigate.
“As of now, nothing has happened,” the group said in an email. “We have to ask ourselves: the Pope, who was for many years the primate of the Argentine church, did he know nothing about clerical abuse in his country?”
Argentine authorities said last week that at least eight children had been abused at the school in Mendoza, but then raised the number to at least 22 after survivors provided testimony through an interpreter. A raid on the school found pornographic magazines, videos and about $34,000 in Fr Corradi’s room, officials said.
“This is a really serious case with irreparable consequences, especially mental and spiritual, for people who are doubly vulnerable, not just because of their age, but also their lack of communication,” said Mendoza Supreme Court prosecutor Alejandro Gulle.
If found guilty, the accused could be sentenced to up to 50 years in prison.