"Any trustee or member of the board of governors who witnessed the tape at any point before it was publicly aired, and took no action, should be removed or resign immediately," he said in a statement.
The scandal has prompted the FBI to investigate whether a former Rutgers basketball employee asked for money from Rutgers in exchange for not making the videos public, a person familiar with the investigation told AP on Sunday.
Asked about the FBI inquiry on Monday, Barchi said the agency wasn't called but came "on their own."
As the investigations mount, Christie said he did not believe that state lawmakers should have an inquiry of their own, saying Rutgers is investigating and that holding hearings would "continue reputational damage" to the school.
Assembly Speaker Sheila Oliver, who has called for hearings, said "the taxpayers, students, faculty, administrators, parents, alumni and other constituents" deserve to know what happened.
Meanwhile, Rutgers is turning to former dean Carl Kirschner to run its athletic department on an interim basis while it conducts a search for someone to take the job permanently.
It's the second time that Kirschner will run the program. He took over at the start of 2009 after Robert Mulcahy was fired, and held the role for four months, stepping down when Pernetti took over.
Zezima, Associated Press writers Tim Sullivan and Tom Canavan contributed to this report from Newark. AP writer Geoff Mulvihill contributed to this report from Haddonfield.
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