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 Jimmy Savile.
Mr Entwistle said that the BBC would conduct an inquiry following a police investigation.
Mr Savile - who died last year - was accused of the sexual abuse of under-age girls in an ITV documentary that aired last week.
Mr Entwistle said that when "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".
Yesterday, British Prime Minister David Cameron called for the allegations to be fully investigated.
Mr Cameron said that the claims in recent weeks from a number of women were "truly shocking".
He said the allegations should be looked into by the BBC - which employed Savile at the time - and, if necessary, by the police.