Huntley, 44, who is serving two life sentences, said that he was "terribly, terribly sorry" and that he had betrayed the people of Soham, Cambridgeshire, in the "worst possible way".
During the search for the girls, Huntley was filmed on television saying he was likely to be the last person to have seen them on the day they disappeared, and expressed sympathy to the families.
They were murdered shortly after entering the home.
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Holly and Jessica had left a family barbecue to walk to a sweet shop when they vanished.
He hid their bodies in his Ford Fiesta before dumping them in woods near RAF Lakenham.
Huntley admitted to deliberately killing Jessica to stop her from speaking after Holly died in the bath in what he says was an accident.
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Huntley's then girlfriend Maxine Carr was sentenced to three-and-a-half years in prison in 2003 after being found guilty of conspiring to pervert the course of justice after giving him a false alibi. He has attempted suicide while in prison.
According to The Sun, he says on the tape: "I can't change anything. I thought about them when they were turning 21 and when they were turning 18".
"I know that, I don't expect it to but I would much rather people have the truth about how I feel".
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