The allegations were reported on Wednesday by The New York Times, The Palm Beach Post and Yahoo News.
This comes after the release of a 2005 tape in which Trump is heard making vulgar comments about women and having a conversation about trying to have sex with a married woman.
One woman told the Times she was seated next to the Republican nominee during a flight to New York some three decades ago, and Trump started groping her suddenly.
“He was like an octopus,” Jessica Leeds, now 74, told the paper. “His hands were everywhere. It was an assault."
Another woman, Rachel Crooks, also told the Times that he kissed her without her permission. “I was so upset that he thought I was so insignificant that he could do that,” she said.
The Trump campaign has denied many of the allegations made against him, and called the Times article "a completely false, coordinated character assassination."
"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," Trump 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,” the statement added.
“None of this ever took place,” Trump told the Times on Tuesday night, and threatened to sue the publication if the paper went ahead to run the story.
“You are a disgusting human being,” he told the reporter, who contacted him before publishing the story. "I don't do it. I don't do it,” he said.
And in a letter to New York Times editor Dean Baquet on Wednesday night, Trump’s lawyer said the article is an attempt to damage Trump's presidential campaign.
“Your article is reckless, defamatory and constitutes libel per se. It is apparent from, among other things, the timing of the article, that it is nothing more than a politically-motivated effort to defeat Mr. Trump’s candidacy,” Marc E. Kasowitz wrote.
After The Washington Post released a recording last week that shows Trump making vulgar remarks about women, Republican officials, including governors, senators and congressmen across the US have disavowed the billionaire.
Trump’s apology for the remarks also failed to quell the unprecedented controversy over his comments, prompting growing demands by Republicans for him to quit the race.
Even Trump’s vice presidential candidate Mike Pence refused to defend the billionaire politician on Saturday, saying that he was “offended” by the obscene comments.
On Monday, however, Pence reiterated his support for Trump, saying he expressed remorse for his controversial comments, Press TV reported.
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