The Cabinet 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 seriously.
Police believe the DJ and television presenter's alleged catalogue of child sex abuse could have spanned six decades and included around 60 victims.
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.
"In terms of a wider inquiry, we have a police investigation on-going at the moment. 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 should be our priority at this stage," she said.
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."
However, Labour leader Ed Milliband last night said the BBC's internal investigations were not enough and called for the Government to set up an independent inquiry into the abuse scandal to "do right by the victims".
BBC director-general George Entwistle offered to appear before the committee next week and said he was sure MPs would take him up on the offer.
Meanwhile, the trustees of Savile's charitable foundation will decide next week whether to still turn his Glencoe cottage into a place of respite for the disabled. Police have not yet approached the trust about searching the property, where the entertainer stayed frequently over more than a decade.