Campaign 2016 Trump: Republican presidential candidate Donald Trump kisses a "Women for Trump" sign during a campaign rally, Wednesday, Oct. 12, 2016, in Lakeland, Florida.
Campaign 2016 Trump: Republican presidential candidate Donald Trump kisses a "Women for Trump" sign during a campaign rally, Wednesday, Oct. 12, 2016, in Lakeland, Florida.

WASHINGTON - Republican presidential candidate Donald Trump said Thursday that allegations by four women that he kissed and touched them inappropriately are "totally and absolutely false."

With his campaign reeling from the accusations, the brash real estate mogul told supporters in Florida, "These claims are all fabricated. They're pure fiction and outright lies. These events never, ever happened and the people who said them fully understand."  He said he has "substantial evidence to dispute" the claims that will be made public at an "appropriate time very soon."

Trump claimed that his opponent in the November 8 election, Democrat Hillary Clinton, and her husband, former President Bill Clinton, "know it and know it very well" that the allegations are not true, but offered no supporting comments. Trump said the national news media was a "political special interest" aligned with the Clinton campaign and published the claims to thwart his run for the White House.

Democratic presidential candidate Hillary Clinton
Democratic presidential candidate Hillary Clinton speaks at a rally at the Smith Center for the Performing Arts in Las Vegas, Oct. 12, 2016.

Trump offered his rebuttal to the incendiary accusations in the hours after the four women alleged that he made unwanted sexual advances on them, just days after he denied acting out on taped boasts he made in 2005 that he could grope women with impunity because he was a celebrity.

The women, in accounts published Wednesday in The New York Times, The Palm Beach Post and People magazine, all described incidents in which Trump, seeking his first elected office, kissed or groped them in unwelcome encounters on an airplane, inside his Trump Tower skyscraper in New York or at his oceanside Mar-a-Lago mansion in Florida.  One of the incidents was more than three decades ago, the others in 2003 and 2005.

Before his remarks at the Florida rally, Trump rebuffed the claims on his Twitter account. "Why didn't the writer of the 12-year-old article in People magazine mention the 'incident' in her story? Because it did not happen!" he said.

He called The New York Times account phony and "a total fabrication."  His lawyers said they were drafting a lawsuit against the newspaper.

WATCH: Trump slams NY Times, media, female accusers

Trump's remarks on the 2005 tape have roiled the late stages of his 2016 presidential race against Clinton, a former U.S. secretary of state. National polls show his support plunging after the widespread broadcast of the tape and his second debate last Sunday with Clinton.

Real Clear Politics, a political web site, said Clinton now has a national 6.2-percentage-point lead less than four weeks before the November 8 election.  In addition, numerous polls show her surging to bigger leads in the key battleground states that will decide the outcome.

The Clinton campaign said the new allegations against Trump "sadly" concur with "everything we know about the way Donald Trump has treated women.  These reports suggest that he lied on the debate stage and the disgusting behavior he bragged about in the tape are more than just words."

In the debate, moderator Anderson Cooper of CNN asked Trump if he had actually done the activities he boasted about on the tape.

"No, I have not," Trump replied, calling his crude remarks "locker room talk."

But two of the women said they reacted angrily when they heard his denial as they, along with more than 60 million Americans, watched the debate unfold on television.

Mindy McGillivray, who says Trump grabbed her rear end while she was assisting a photographer at an event at his Florida estate in 2003, said she got off her couch at her home and yelled at the TV, "You liar!"

Jessica Leeds arrives at her apartment building, O
Jessica Leeds, one of the women who accuse Republican presidential candidate Donald Trump of unwanted sexual advances, arrives at her apartment building in New York, Oct. 12, 2016. Leeds alleges that Trump repeatedly groped her on a flight to New York more than 30 years ago.

Another woman, Jessica Leeds, now 74, told the Times, "I wanted to punch the screen."  She alleged that Trump, in the first-class cabin on a flight to New York more than 30 years ago, sat beside her and suddenly lifted the armrest between them, grabbed her breasts and tried to put his hand up her skirt.

"He was like an octopus," she recalled. "His hands were everywhere."

Leeds said she fled to the back of the aircraft.  "It was an assault," she said.

In the other incidents, Rachel Crooks, then a 22-year-old receptionist, said that in 2005 she encountered Trump at his office building in New York, introduced herself and shook hands with him.  But she said Trump wouldn't let go and began kissing her cheeks and then "kissed me directly on the mouth."

"It was so inappropriate," Crooks said.  "I was so upset that he thought I was so insignificant that he could do that."

The fourth woman, Natasha Stoynoff, a People reporter assigned to cover Trump for the gossipy, celebrity magazine, said while she was at Mar-a-Lago in 2005 interviewing Trump and his then-pregnant wife Melania, he found a moment when his wife was elsewhere changing clothes to take her into a room and shut the door.

"Within seconds," Stoynoff recalled, "he was pushing me against the wall and forcing his tongue down my throat."

"I was stunned," she said.  "And I was grateful when Trump's longtime butler burst into the room a minute later, as I tried to unpin myself.  How could the actions of one man make me feel so utterly violated?  I'd been interviewing A-list celebrities for over 20 years, but what he'd done was a first.  Did he think I'd be flattered?"

She said that afterward Trump added, "You know we're going to have an affair, don't you?"

The women's descriptions of Trump's advances on them come close to the way he depicted himself in 2005, remarks captured on a live microphone as he rode on a bus on a Hollywood back lot as he headed to a cameo appearance on a television soap opera.

"I just start kissing them," he told a celebrity television host.  "It's like a magnet.  Just kiss.  I don't even wait.  And when you're a star, they let you do it.  You can do anything."  Trump said he would just grab women's genitalia.

First lady Michelle Obama, in a campaign appearance Thursday for Clinton in New Hampshire, denounced Trump's comments, calling them "an insult to decent men."

"This isn't about politics," she said.  "It's about human decency.  The men in my life do not talk about women this way."

Referring specifically to the Times account, the Trump campaign 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 the campaign for president should say it all."

Attorneys representing Trump sent a letter to Times Executive Editor Dean Baquet demanding the newspaper remove the article from its website and issue an apology.

"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."

The newspaper stood by its story and said it would "welcome the opportunity" to have a court fight over publication of the article.

Trump has often criticized the media's reporting on his campaign, including singling out what he calls the "failing New York Times."