Justice Secretary Chris Grayling has said he is not convinced by the case for an immediate judge-led inquiry of the kind Harriet Harman has proposed.
Mr Grayling told BBC1's Andrew Marr Show: "There is always a danger if you set up a very substantial inquiry process of that kind that it takes much longer to get to the truth.
"What should be happening right now first and foremost...is we should be looking to see who is still around who was involved, and criminal proceedings should follow if people were guilty of participating in these offences alongside Jimmy Savile. That is of paramount importance."
Mr Grayling accepted that the case indicated that the authorities did not pay enough attention to the complaints of abuse victims in the past.
"I hope every single person in the law enforcement world today is accepting the fact that things went badly wrong and it should not happen again," he said.
Mr Grayling added: "Clearly what has happened is absolutely horrendous. It is shocking. There was clearly a culture that should never, ever, ever have been allowed to exist."
Amid the fallout from the Jimmy Savile scandal the BBC is investigating nine allegations of sexual harassment among staff and contributors.
BBC boss George Entwistle has spent almost two hours taking questions from MPs about the corporation's handling of the Savile scandal.
Ex-BBC boss Mark Thompson has told ITV News he will help with any inquiry into the corporation and its handling of the Savile allegations.