Charles Clarke, who took over as Home Secretary after Mr Blunkett's resignation, has received an apology for remarks made in the biography.
The former education secretary said that Mr Blunkett - who had accused him of "going soft" and taking "his foot off the accelerator" - had accepted that the remarks were untrue.
Asked on Radio 4's Today programme why the outgoing home secretary had made them, Mr Clarke said: "Presumably because that is what he felt at the time.
But I am a great supporter of David Blunkett, I always have been."
He rejected Deputy Prime Minister John Prescott's view that Mr Blunkett was arrogant. "Every politician needs an element of self-confidence," he said.
"Perhaps over self-confidence."