E. Jean Carroll, 75, a television show host and magazine columnist, made the accusation in an essay published on Friday in NY Magazine, the local media reported.
The President said he has never met Carroll and the writer's motivation behind the claim was to "sell a new book", reported BBC news.
"I've never met this person in my life," the US President said in a statement. "She is trying to sell a new book-that should indicate her motivation. It should be sold in the fiction section."
Trump encouraged anyone with "information that the Democratic Party is working with Carroll or New York Magazine" to notify the White House.
He accused the publication of "peddling fake news".
"Shame on those who make up false stories of assault to try to get publicity for themselves, or sell a book, or carry out a political agenda," he said.
"It's just as bad for people to believe it, particularly when there is zero evidence," he added.
In his statement, Trump thanked Bergdorf Goodman for "confirming they have no video footage of any such incident".
Carroll has said that the rape happened in a Bergdorf Goodman changing room, in New York, in the mid 1990s.
Trump had greeted her as: "Hey, you're that advice lady!" to which she replied: "Hey, you're that real-estate tycoon!"
He then sought her help to buy a gift for a woman.
Both settled on a gift of lingerie, and when he asked her to model it, she jokingly said he must try it on first, a leading media outlet reported.
Carroll, the 16th woman to accuse Trump of sexual assault, wrote that inside the changing room, he had pinned her to the wall.
"He opens the overcoat, unzips his pants, and, forcing his fingers around my private area, thrusts his penis halfway - or completely, I'm not certain - inside me.
"It turns into a colossal struggle.
"I finally get a knee up high enough to push him out and off and I turn, open the door, and run out of the dressing room."
( With inputs from IANS )