BBC Director General George Entwistle has 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, and 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.

Mr Cameron said 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 the allegations should be looked into by the BBC - which employed Savile at the time - and, if necessary, by the police.

Mr Entwistle said there needed to be a "comprehensive examination" of what went on, following the police investigation, telling 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 properly."

Mr 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 on and whether anybody around Jimmy Savile knew what was going on".

Mr Entwistle said he was told Newsnight was looking at a possible investigation into Savile in 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 judgment 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, 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."