BBC Director General George Entwistle today said he would like to "apologise on behalf of the organisation" in the wake of the allegations of sexual abuse against former DJ Sir Jimmy Savile.
He also confirmed the BBC would conduct an inquiry following a police investigation.
He spoke out a day after Prime Minister David Cameron called for allegations of sexual abuse against the late celebrity to be fully investigated.
Cameron said that the claims from a number of women which have emerged over recent weeks that they were abused by Savile as teenagers were "truly shocking".
And he said that the allegations should be looked into by the BBC – which employed Savile at the time – and, if necessary, by the police.
ded to be a "comprehensive examination" of what went on, following the police investigation.
He told BBC Radio 4's Today programme: "These are awful allegations that have been made and they are criminal allegations and the first thing I want to say is that the women involved here have gone through something awful, something I deeply regret they should have to go through and I would like to apologise on behalf of the organisation to each and every one of them for what they've had to endure here."
He added: "When the police have finished everything they have to do and when they give me an assurance that there is no danger of us in any way compromising or contaminating an investigation, I will take it further and ensure that any outstanding questions are answered properlly.
Entwistle said any investigation needed to be done in "two phases", and the BBC would "take a look properly" after the police inquiry.
He said: "At the heart of what went on are a series of criminal allegations about the behaviour of Sir Jimmy Savile, Now, the way to deal with those is to make sure that the police, who are the only properly constituted authority for dealing with criminal investigations, are allowed to make the examinations and inquiries they need to make.
"So… it is critically important that we start by putting the BBC at the disposal of the police in this regard."
Any BBC probe, he added, would examine the "broad question of what was going and whether anybody around Jimmy Savile knew what was going on".
Entwistle said he was told that Newsnight was looking at a possible investigation into Savile at around early December last year.
He said: "The BBC is designed in such a way that news and current affairs programmes are protected from the interests and influence of the rest of the organisation."
He added: "With the benefit of hindsight I think we could all wish that Newsnight had been able to go as far as ITV went."
But he also stressed he was supportive of the judgement made in relation to the programme based on knowledge at the time.
Asked why the BBC ran a eulogy on Savile after evidence surfaced, he said: "I didn't know what had become of that investigation, I didn't know what discoveries, if any, that they had.
"A great many people in the country loved Jimmy Savile and wanted to contribute to that programme."
Asked if he had heard about the rumours about Savile at the time the programme was broadcast, he said: "No, I had not. Jimmy Savile was regarded as, I think by a great many people, as odd, a bit peculiar, that was something I was aware some people believed, but I did not know, and I've heard an awful lot of talk from people about what they knew, and it does seem to me that if people knew, they'd seen something themselves or been told something directly or had evidence of his behaviour, if they knew that then there was an enormous obligation on them to have done something about it."
The BBC of today, he added, has a child protection policy which would "absolutely stop" access for people in Savile's position to under-18s on BBC premises.
He said: "It's very important that people don't think the BBC of today is anything like in character managed the way it was at the time."
Former Radio 1 DJ Liz Kershaw has described how she was routinely groped by another presenter as she was broadcasting.
Kershaw, who now works for Radio 6 Music, said that when she joined Radio 1 in 1987 – the year Savile left – his behaviour was an "open secret" at the station.
TV and radio presenter Sandi Toksvig has also told how she was groped on air by a "famous individual" 30 years ago.
Toksvig, who declined to name the celebrity, said when she informed other staff what had happened they thought it was funny.
Police child abuse officers have met BBC officials to discuss allegations over Savile, Scotland Yard said earlier.
The police said they were contacting all individuals who have made claims about the late presenter and should know how many victims there are some time this week.
Scotland Yard is currently considering a number of claims, including a historic rape allegation referred to Met officers by Surrey Police.
St Albans Tory MP Anne Main has also written to Lord Justice Leveson asking him to investigate how the BBC handled the allegations as part of his inquiry into press standards.
A growing number of victims have come forward to allege that Savile sexually assaulted them after five women took part in a documentary claiming that they had been abused.
In the film, screened last Wednesday, the alleged victims accused the Jim'll Fix It presenter of sexually assaulting them, some while on BBC premises.
Police in Northamptonshire have been contacted by two alleged victims, while it emerged last week that Surrey, Sussex and Jersey Police have also received complaints.
The Met said the assessment of claims will be led by Detective Superintendent David Gray, from the force's Child Abuse Investigation Command.
Broadcaster Janet Street-Porter previously revealed that she was aware of rumours about the television and radio presenter's alleged abuse of under-age girls when she worked at the BBC in the late 1980s.
The journalist also said there was a culture of inappropriate behaviour behind the scenes of the "male-dominated" entertainment industry, adding that nothing would have been done even if the allegations about the late Top Of The Pops host were raised.
Tory MP Rob Wilson welcomed the investigations announced by Mr Entwhistle after earlier writing to the BBC Trust chairman Lord Patten.
But he told the BBC News channel: "This goes much wider than criminality, this goes to a culture that seemingly existed and this is said by people who were in that environment at the time, a culture that existed which was a pretty rotten culture, that allowed young girls to be molested and worse and presenters to be fondled by other celebrities.
"This is an incredible situation and needs to be investigated fully."