The Time's report, and additional claims published in other media, saw at least half a dozen women step forward after a video emerged last week showing the brash billionaire boasting about grabbing women's genitals and forcing himself on them.
Trump has denied he ever committed sexual assault and launched a defiant attack on US media Thursday, dismissing the published accounts as "pure fiction."
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"The essence of a libel claim, of course, is the protection of one's reputation," Times vice president and assistant general counsel David McCraw wrote in a letter to Trump's lawyer, who demanded a full retraction and apology from the newspaper.
"Nothing in our article has had the slightest effect on the reputation that Mr Trump, through his own words and actions, has already created for himself."
McCraw noted the presidential candidate's lewd comments about women and some women's public comments about his unwanted advances.
"But there is a larger and more important point here. The women quoted in our story spoke out on an issue of national importance. It would have been a disservice not just to our readers but to democracy itself to silence their voices," he said.
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"We did what the law allows: We published newsworthy information about a subject of deep public concern.
"If Mr Trump disagrees, if he believes that American citizens had no right to hear what these women had to say and that the law of this country forces us and those who dare to criticize him to stand silent or be punished, we welcome the opportunity to have a court set him straight."
Trump's campaign has been in free-fall since last week's release of the damning tape.
The allegations published against Trump suggest a pattern of sexually inappropriate behavior towards women.
Jessica Leeds, a 74-year-old former businesswoman, told the Times that Trump groped her on a flight in the early 1980s as they sat next to each other in first class, grabbing her breasts and trying to put his hand up her skirt.
"He was like an octopus," Leeds told the daily.
"His hands were everywhere," she added. "It was an assault."
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A second accuser, Rachel Crooks, said she was a 22-year-old receptionist at a real estate company in Trump Tower in 2005 when she encountered Trump outside an elevator one morning.
After she introduced herself, he "kissed me directly on the mouth," she told the Times.
"It was so inappropriate," Crooks added. "I was so upset that he thought I was so insignificant that he could do that."
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