By Agence France-Presse
The Post reported that a woman shared a dramatic story -- which could not be substantiated -- that Moore impregnated her when she was a teenager in 1992 and that she later had an abortion.
But it said the woman, who was interviewed several times over two weeks, was seen entering the New York offices of Project Veritas, an organization which targets mainstream media organizations.
Moore's alleged misconduct came to light after an investigation by the Washington Post, which recounted stories of women who claimed Moore molested or harassed girls as young as 14.
Moore has denied the allegations and has rejected pressure from fellow Republicans to drop out of the special election to be held in December.
On Monday, the Post said it did not publish an article based on the woman's allegations, noting inconsistencies in her story and an online post which cast doubts on her motivations.
The newspaper did publish a nine-minute interview with the woman, identified as Jaime Philips, with a Post reporter.
The Post said she denied working with any organization but that reporters witnessed her entering Project Veritas, which uses secret recordings intended to expose media bias.
Project Veritas did not immediately respond to an AFP request for comment.
The Moore allegations have touched off a political firestorm, with his backers claiming he has been the target of political opponents even as his poll numbers fall.
The Post said it decided to release the woman's comments despite an earlier agreement to be "off the record."
"We always honor 'off-the-record' agreements when they're entered into in good faith," executive editor Martin Baron was quoted as saying.
"But this so-called off-the-record conversation was the essence of a scheme to deceive and embarrass us. The intent by Project Veritas clearly was to publicize the conversation if we fell for the trap. Because of our customary journalistic rigor, we weren't fooled, and we can't honor an 'off-the-record' agreement that was solicited in maliciously bad faith."