University President Robert Barchi, speaking during a town hall meeting on the school's Newark campus, said that he wants any instances of bullying or homophobic language to be immediately reported.
Barchi reiterated that he wished he had viewed the video where Rice shoved players and called them gay slurs when it first surfaced in November, saying he would have fired Rice then.
Meanwhile, Gov. Chris Christie on Monday defended Barchi's handling of the scandal, as the university announced it plans to commission an independent probe of what happened.
While he's issued statements, a news conference Monday was the first time Christie answered questions about the situation.
He said that ousting Barchi now would be a mistake for Rutgers, and he praised the president, who took office in September, for working quickly last week to fire men's basketball coach Mike Rice and get Athletic Director Tim Pernetti to resign within days after he - and the public - first viewed a video of Rice's behavior in practices from 2010 through last year.
Christie said Rice should have been ousted last year when university officials, including Pernetti, a university lawyer who has since resigned and a member of the school's board of governor's first saw the video - if not sooner.
"They were wrong not to come to the conclusion that Coach Rice needed to be fired immediately," Christie said. The Republican governor added that had he been aware of the issues earlier he would have used his "power of persuasion" to try to get Rice fired then.
Christie said it was a mistake for Barchi, who took office in September, not to watch the video last year when he first was told about it. But he said presidents must delegate some matters and that the mistake was not a firing offence.
Also Monday, Rutgers announced that it is commissioning an independent review of Rice's conduct the way the university handled the situation.
The scandal has prompted the FBI to investigate whether a former Rutgers basketball employee asked for money from Rutgers in exchange for not taking the videos public, a person familiar with the investigation told The Associated Press.
Rutgers said its Board of Governors will meet Thursday to discuss hiring the independent adviser to review the case.
Also Monday, board chairman Ralph Izzo said that one board member - athletics committee chairman Mark P. Hershhorn - had seen the video in December. Izzo said that it was not shown to other members and while the topic of the coach's conduct was discussed at a committee meeting in December, it was not discussed at the whole-board meeting that month. The university did not immediately respond to a request to interview Hershhorn.
Barchi on Monday appeared at a town hall meeting on the university's Newark campus. He had canceled a similar event scheduled for last week as he dealt with the athletic department scandal. In his remarks Monday, he did not mention the coach.
Instead, he focused solely on a reconfiguration of higher education in New Jersey.