Harriet Harman has said she "regrets" a civil liberties group she once worked for had links to pro-paedophile campaigners in the 1970s but insisted she has "nothing to apologise for".
The National Council for Civil Liberties granted "affiliate" status to the Paedophile Information Exchange.
The Daily Mail has urged the deputy Labour leader to explain this link.
But Ms Harman has accused the newspaper of "smear and innuendo" and said it "should be apologising".
From 1978 to 1982 Ms Harman was legal officer at the National Council for Civil Liberties, which was the predecessor to campaign group Liberty.
The Paedophile Information Exchange (PIE) - a group that spoke positively about adults attracted to children - was granted affiliate status with the National Council for Civil Liberties in 1975.
In a TV interview, Ms Harman 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.
"It is actually not me that should be apologising for something that I haven't done. It is the Daily Mail that should be apologising for their smear and innuendo."
Appearing on BBC Two's Newsnight on Monday, she repeatedly sidestepped questions about whether it had been a mistake to allow the Paedophile Information Exchange to be affiliated to the civil liberties group.
She said her work had always been "to protect children, especially from child abuse".
Ms Harman also said anyone could apply to join the National Council for Civil Liberties upon payment of a fee, and it had had about 6,000 members and nearly 1,000 affiliated organisations when she joined.
The newspaper has said she "tried to water down child pornography laws" during her time at the National Council for Civil Liberties.
Her husband, Labour MP Jack Dromey, who also used to work at the National Council for Civil Liberties, has insisted he had made "repeated public condemnations" of the pro-paedophile group.
Former Labour Health Secretary Patricia Hewitt, who was the National Council for Civil Liberties' general secretary from 1974 to 1983, has also featured in the Daily Mail's coverage but has yet to comment on the story.
BBC chief political correspondent Gary O'Donoghue said the "central point" was the "extent to which people in NCCL did push back against this organisation".
He said PIE had "got in on the act" of a debate over the age of consent for homosexuals, and there was a question about whether people in NCCL were "culpable in letting them" do so.
The Daily Mail's consultant editor Andrew Pierce told the BBC the trio needed to answer why they had "in any way" allowed the National Council for Civil Liberties to associate with the Paedophile Information Exchange.
"It is not a smear to keep asking the same question," he said.
But Ms Harman attempted to fight back, tweeting the message "when it comes to decency and sexualisation of children, would you take lessons from the Daily Mail?" alongside a photograph of a Daily Mail website article featuring a picture of a 12-year-old in her "first bikini shoot".
Asked about the row, Deputy Prime Minister Nick Clegg said it was up to Ms Harman to "speak for herself about what happened in the 1970s".
But he said the current head of Liberty had been right to dissociate it from what "is clearly an abhorrent organisation".
The National Council for Civil Liberties was founded in 1934 as a result of fears that the right to peaceful protest was under threat.
The Paedophile Information Exchange was an international organisation of people who traded obscene material.
It made national newspaper headlines in the early 1980s when members faced charges of publishing and sending articles through the post, and was disbanded in 1984.
Its ex-leader reportedly said paedophilia was "as much a healthy part of the natural diversity of our species as red hair or left-handedness".