George Entwistle offered a "profound and heartfelt apology" to victims, whose number has risen to a potential 40, covered by 14 different police forces from around the UK.
Entwistle has ordered two "forensic and soul searching" independent inquiries to probe allegations of child abuse by its former presenter Savile.
The first BBC inquiry will examine the catalogue of abuse by Savile over his four-decade career, covering what Entwistle described as the "culture and practices" of the BBC in the "years Jimmy Savile worked here and afterwards".
The second will investigate whether any BBC executives, including Entwistle, improperly interfered with an axed Newsnight investigation into Savile last year.
The point is to deal with "the cloud of suspicion that cannot be allowed to continue," he said at a press conference.
But the BBC will not review the editorial decision by Newsnight editor Peter Rippon to drop the film.
"I have made clear my revulsion at the thought that these criminal assaults were carried out by someone employed by the BBC and that some may have happened on BBC premises as well, we now discover, in hospitals and other institutions," Entwistle said.
The BBC efforts to get a grip on the scandal came as the Metropolitan police revealed that the catalogue of abuse claims had spiralled in 72 hours.
Scotland Yard said it was pursuing 340 potential lines of inquiry into sex abuse claims.
Savile, known for his cigars and jangling jewellery, died in October last year aged 84.
Celebrities and former BBC staff potentially face arrest for alleged sex offences as police hunt accomplices of Savile's four decades of attacks.
He is alleged to have raped and molested children as young as ten.
As well as the BBC, three National Health Services hospitals, a former children's home in Jersey and a now-defunct school in Surrey are accused of giving him free rein to attack children.
Some victims have named people "around Savile" as being complicit in his abuse.
The developments came after a TV director who reported Savile to BBC bosses decades ago, when he caught the star having sex with a 15 to 16-year-old girl in his dressing room, revealed he was ignored.
David Nicolson, 67, who had been a director on Jim'll Fix
it, said he made several attempts to expose Savile to the BBC, but was told: "That's Jimmy" and "that's the way it goes".
Savile also allegedly molested vulnerable children at Leeds General Infirmary, including a brain-damaged girl, as well as Stoke Mandeville Hospital and Broadmoor Hospital.
In a statement, the Metropolitan Police said "the Metropolitan Police Service have to date received 340 potential lines of enquiry since they took the national lead in relation to allegations concerning Jimmy Savile last week.
"Since October 4, we are in contact with 40 potential victims. We have officially recorded 12 allegations of sexual offences but expect this number to grow. We continue to liaise with 14 forces," the statement said.
"Officers from the Serious Case Team of the MPS Child Abuse Investigation Command will continue to contact those who have come forward, to ensure that they are given the advice and support they need," it added.
Meanwhile the Department of Health is to investigate how Jimmy Savile was allowed to work as a volunteer following allegations that he abused and raped patients at Broadmoor hospital in the 1970s and 1980s.
A spokeswoman said there would be an investigation into how the TV presenter was appointed to lead a "taskforce" overseeing a restructuring of the hospital's management.
In a statement, the department said: "We will investigate the Department of Health's conduct in apparently appointing Savile to this role."
"Although the framework for child protection and safeguarding for Broadmoor and other special hospital patients changed radically in 1999, we of course want to establish the circumstances and see if any lessons can be learned," the statement said.
"In hindsight, he should very obviously not have been appointed. Had anyone involved in the appointment been aware of allegations of abuse against Savile, we would not have expected him to have been appointed," it added.
Savile, who raised millions of pounds by running marathons and half-marathons, has now been removed from the Great North Run's hall of fame.
London: Expressing "profound apology" to Jimmy Savile's child abuse victims, BBC Director-General has ordered two "forensic and soul searching" independent inquiries in to allegations of assault by the late TV presenter.
First Published: Saturday, October 13, 2012, 21:11