Two women have come forward claiming that Donald Trump molested them in public, one saying she was groped on an airplane and another saying he aggressively kissed her outside an elevator in Trump Tower, according to a report Wednesday.

The women said they were outraged that Mr. Trump in the debate Sunday denied ever acting on his boast, caught on a hot mic in 2005, that he can kiss and fondle women at will because he is a celebrity, the New York Times reported.

Mr. Trump, the Republican presidential nominee, called the report “fiction.”

“This entire article is fiction, and for the New York Times to launch a completely false, coordinated character assassination against Mr. Trump on a topic like this is dangerous,” Trump campaign spokesman Jason Miller said in a statement.

“To reach back decades in an attempt to smear Mr. Trump trivializes sexual assault, and it sets a new low for where the media is willing to go in its efforts to determine this election,” he said.

“It is absurd to think that one of the most recognizable business leaders on the planet with a strong record of empowering women in his companies would do the things alleged in this story, and for this to only become public decades later in the final month of a campaign for president should say it all,” said the statement.

“Further, the Times story buries the pro-Clinton financial and social media activity on behalf of Hillary Clinton’s candidacy, reinforcing that this truly is nothing more than a political attack. This is a sad day for the Times,” it said.

Mr. Trump’s campaign already was reeling from the 2005 video tape that surfaced Friday. The tape’s audio caught Mr. Trump talking lewdly about women and his sexual exploits in a private conversation with “Access Hollywood” host Billy Bush.

He has insisted it was just “locker room talk” and he never acted that way.

A spokeswoman for Hillary Clinton, the Democratic nominee, said the story about he two women sounded believable.

“This disturbing story sadly fits everything we know about the way Donald Trump has treated women. These reports suggest that he lied on the debate stage and that the disgusting behavior he bragged about in the tape are more than just words,” Clinton campaign communications director Jennifer Palmieri said in a statement.

According to the report, Jessica Leeds, 74, said that a decade ago she was seated beside Mr. Trump in the first-class cabin of a commercial airplane when, about 45 minutes into the flight, the real estate tycoon lifted the armrest and began to touch her.

Ms. Leeds claimed that he grabbed her breasts and tried to put his hand up her skirt.

“He was like an octopus,” she told the newspaper. “His hands were everywhere.”

Ms. Leeds said that she fled to the back of the airplane to escape him.

Rachel Crooks said that in 2005, when she was 22 and working as a receptionist at a real estate investment office in Trump Tower in Manhattan, Mr. Trump forced himself upon her.

Ms. Cook said she encountered Mr. Trump outside an elevator and introduced herself. When they shook hands, he wouldn’t let go and then began kissing her cheeks, according to the newspaper.

He then kissed her “directly on the mouth,” she said, adding that she was badly shaken by Mr. Trump’s inappropriate behavior.

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