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He said the women making the allegations were “horrible liars” and the media was colluding with rival Hillary Clinton.
Several women say Donald Trump groped them or forcibly kissed them.
First Lady Michelle Obama earlier said Donald Trump’s boasts about groping women were “shocking and demeaning”.
“Leaders should meet a basic standard of human decency,” she said during a campaign appearance in New Hampshire.
Seeing Donald Trump make inappropriate comments about women, on a video leaked last week to the Washington Post, “has shaken me to my core in a way that I cannot have predicted,” Michelle Obama said, her voice cracking with emotion.
The first lady never mentioned Donald Trump by name but her references made her target obvious.
Two women told the New York Times that Donald Trump groped or kissed them.
A People magazine reporter also said she was forcibly kissed, while another woman said Donald Trump grabbed her bottom.
Making his first public appearance since the allegations were made, Donald Trump told a rally in West Palm Beach these stories were “a conspiracy against the American people” by the political and media establishment.
Donald Trump said he had evidence the accusations were unfounded and would release that at the “appropriate time”.
In one reference, the Republican presidential runner appeared to imply People magazine writer Natasha Stoynoff could not have been telling the truth because of her appearance.
“Take a look. You take a look. Look at her, look at her words, you tell me what you think. I don’t think so, I don’t think so.”
The media, Donald Trump said, “will seek to destroy your career and your family”.
Donald Trump has threatened to sue the New York Times, which published accusations from two women on October 12.
The publication has responded by saying it would welcome the opportunity to make its case in court.
Many of the women said Donald Trump’s denial during the second presidential debate prompted them to come forward.
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