Ms Harman said she was the victim of a "politically-motivated smear campaign" by the Daily Mail, saying she had "done nothing wrong".
"They have accused me of being an apologist for child sex abuse, of supporting a vile paedophile organisation, of having a relaxed attitude to paedophilia and of watering down child pornography laws. These are horrific allegations and I strongly deny them all of them," she said.
Ms Harman and her MP husband Jack Dromey broke their silence after the newspaper ran a series of stories about their actions while officials at the National Council for Civil Liberties (NCCL) in the 1970s.
The body granted 'affiliate' status to the Paedophile Information Exchange (PIE), and is said to have lobbied for loosening of laws.
Ms Harman said: "The editor and proprietor of the Daily Mail are entitled to their political views and they are of course entitled to oppose what I stand for but they are not entitled to use their newspaper to smear me with innuendo because they disagree with me politically and hate my values."
Ms Harman denied that she had ever supported lowering the age of consent to 10, scrapping the law on incest, or sought to water down the law on child pornography.
Ms Harman said she had gone to work for the NCCL because she had supported its work on gender and racial equality, and against domestic violence.
Labour strategists are understood to have decided they needed to tackle the allegations "vigorously", as they did after the Mail criticised Ed Miliband's late father Ralph last year.
Mr Dromey - a shadow home affairs spokesman - said the allegations were "beneath contempt".
"Sexual abuse of children is evil and I have always viewed paedophiles and any group associated with them as evil," he said.