Culture secretary Maria Miller has criticised the BBC for failing to broadcast its own television investigation into allegations against the presenter.
The minister told MPs the corporation had acted "inappropriately" when it pulled a Newsnight film into sex abuse claims against the late DJ and broadcaster but said she was "now confident" BBC chiefs were taking the claims "very seriously". However, she dismissed calls for an independent inquiry.
Labour deputy leader Harriet Harman said there was widespread "revulsion" that the allegations of systemic assaults took place at the beloved "aunty", the affectionate nickname for the institution, and claimed the the star's "exalted" status allowed him to act with impunity.
Ms Miller said the allegations had "wide-ranging implications for a number of public institutions" but rejected calls for an outside inquiry to restore the public's faith, warning it could hamper police investigations.
"In terms of a wider inquiry, we have a police investigation on-going at the moment," she said. "Everybody would agree that it is really important that those individuals who have been victims know that that investigation can go on unfettered and that that should be our priority at this stage."
She added: "The BBC has launched three separate investigations, as the House will be aware. The first will look particularly at the allegations with regard to the item on Savile which was inappropriately pulled from Newsnight."
Ms Harman said: "What has deepened the revulsion is that this happened at the BBC, an institution so loved and trusted it is known as aunty.
"This has cast a stain on the BBC."
Commons culture committee chairman John Whittingdale said the director-general George Entwistle had offered to appear before the committee next week and said he was "sure" MPs would take him up on the offer.
Leeds North East Fabian Hamilton said his constituents, who turned out in their thousands to pay tribute to the present when he died, felt "betrayed and angry".
Police believe the DJ and television presenter's alleged catalogue of child sex abuse could have spanned six decades and included around 60 victims.
Mr Entwistle announced last Friday that two inquiries would be launched into the abuse claims. One will look into whether there were any failings over the handling of the abandoned Newsnight piece. A second independent inquiry will look into the "culture and practices of the BBC during the years Jimmy Savile worked here", Mr Entwistle said.
Conservative MP Rob Wilson, who secured the urgent question in the Commons, said the BBC had been "slow to react" to the scandal and accused its Trust of acting as a "cheerleader and defender".
"I have a number of major concerns that the inquiries by the BBC will not be sufficiently independent, transparent and robust to give the public confidence," he said.
Any hint of a cover-up by the BBC of its own role in this dreadful affair will cause huge damage to public and audience trust."
The Department for Culture, Media and Sport rejected suggestions Ms Miller had prejudged the outcome of the BBC inquiry.
"The secretary of state has not prejudged the outcome of the BBC's investigation into the pulling of a Newsnight item on Savile," a spokesman said.
"As the secretary of state made clear in the House, it is for the BBC, not ministers, to investigate these allegations."