Colleagues of the deputy Labour leader said the paper was mounting a "witch-hunt" while Ed Miliband made clear he backed the London MP "100%".
Ms Harman said she had never "colluded" with the Paedophile Information Exchange (PIE) as the legal officer at the National Council for Civil Liberties(NCCL) in the 1970s.
The Labour frontbencher called for an apology from the Daily Mail - which has highlighted links between PIE and the NCCL - for running what she described as a campaign of "smear and innuendo" against her.
Last year, Mr Miliband clashed with the tabloid after it branded his late father, Ralph Miliband, a Marxist academic, as the "man who hated Britain".
Ms Harman issued her statement of regret after a bruising TV interview in which she repeatedly refused to say it had been a "mistake" for the NCCL to have allowed PIE to become an affiliate member in the 1970s.
Yesterday, she said: "I'm not going to apologise because I've got nothing to apologise for. I very much regret that this vile organisation, PIE, ever existed and that it ever had anything to do with NCCL, but it did not affect my work at NCCL."
She added: "They had been pushed to the margins before I actually went to NCCL and to allege that I was involved in collusion with paedophilia or apologising for paedophilia is quite wrong and is a smear."
But, Andrew Pierce, Daily Mail consultant editor, said Ms Harman and her husband Jack Dromey MP - who was also prominent in the NCCL - should have done more to disassociate the civil rights body from PIE. He said: "It matters enormously that they did not do more to get rid of this horrible, disgusting organisation."