Gonzales-Mugaburu, 59, is accused of sexually abusing seven boys under his care, one as young as 8 years old, according to the Suffolk County District Attorney's office.
He pleaded not guilty at an arraignment in Suffolk County Court on Friday morning.
"We believe there are many more victims and we are asking them to come forward, even if the crimes happened many years ago," Suffolk County District Attorney Thomas Spota said Friday.
In a bail hearing and at a news conference that followed, prosecutors described the "house of horrors" that Gonzales-Mugaburu ran for the dozens of foster children he took into his Ridge, New York, home.
"The boys told detectives they were not permitted access to phones, and as they got older, they were not permitted to have girlfriends or any visitors," Spota said.
"They were only permitted two meals per day, which they were required to eat while sitting on the floor, and Mugaburu disciplined the children by forcing them to stand outside in the cold and rain," Spota said.
Daniel Driscoll, an attorney for Gonzales-Mugaburu, did not respond to a request for comment Friday afternoon.
Bond was set at $1 million and Gonzales-Mugaburu remains incarcerated in the Suffolk County Correctional Facility, according to the district attorney's office.
If convicted of all charges, Gonzales-Mugaburu faces 50 years in prison.
Gonzales-Mugaburu was arrested in January after a caseworker told Suffolk County police that two of his foster children, 11 and 13 years old, had complained that Gonzales-Mugaburu regularly made sexually inappropriate remarks to them, the district attorney's office said.
A grand jury indictment unsealed Friday morning charged Gonzales-Mugaburu with 17 counts over a variety of sexual criminal conduct charges related to incidents from 1996 to 2015.
The ages of the alleged victims ranged from 8 to 20, Spota said.
Most of the children under Gonzales-Mugaburu's care were from New York and placed by the New York City Administration for Children's Services, in association with St. Christopher Ottilie, a New York family services organization, according to the district attorney's office.
In a statement, the NYC Administration for Children's Services said they were "deeply troubled" to learn of the allegations and that upon hearing them, they immediately removed the children from Gonzales-Mugaburu's home.
"While any child experiencing abuse in foster care is one too many, the vast majority of foster parents are taking good care of the children in their care," Deputy Press Secretary Carol Cáceres said. "We are committed to cooperating with the authorities throughout this investigation."
Rose Anello, chief strategy officer for St. Christopher Ottilie Family of Services, also said her organization is cooperating with authorities and that "SCO considers the safety and well-being of children in our programs to be our absolute highest priority."
Anello said SCO had placed 71 children in Gonzales-Mugaburu's home.