In a telephone interview with the BBC from an Austrian prison, Irving said he accepted that 1.4 million Jews were killed at the so-called Reinhard extermination camps of Sobibor, Belzec and Treblinka, but he insisted 1.1 million Jews could not have been executed at Auschwitz.
"The Anne Frank family wasn't gassed, although they were in Auschwitz," he said. "When they fell ill, they were looked after by SS doctors, and two of them survived. The whole Anne Frank story is proof that I am right."
Irving was sentenced to three years in prison after his one-day trial in Vienna last week, where he pleaded guilty to denying the Holocaust in two speeches made to Austrian neo-Nazis in 1989.
He now spends 23 hours a day in solitary confinement. Austrian prosecutors are seeking to extend his sentence to 10 years because of Irving's "special importance to right-wing radicals," The Times of London reported.