Washington (CNN) Liberty University President Jerry Falwell Jr., head of the world's largest evangelical campus, said Donald Trump told him he has email evidence proving women making accusations of touching them inappropriately and without consent are lying.

"I talked to Mr. Trump late last night and he explained why they were not true," Falwell said about the GOP nominee Thursday on CNN's "At This Hour." "I think his statement will be very strong in a few minutes when he comes out (to speak)."

In a New York Times story published Wednesday, Jessica Leeds claims Trump grabbed her breasts and tried to put his hand up her skirt while the two were on an airplane more than three decades ago. Leeds said she had never met Trump before.

In a separate allegation, Rachel Crooks says that while working in Trump Tower 11 years ago at a company that he did not own, he kissed her outside an elevator after she introduced herself. Trump told The New York Times of both incidents: "None of this ever took place."

Falwell said he spoke with Trump Wednesday night after appearing on CNN's "OutFront with Erin Burnett." Falwell did not elaborate on what specific evidence Trump had against his accusers, besides saying that they were "emails" where the women in the story had asked Trump for jobs.

"He told me about emails he had from these accusers who wanted to work for him after the supposed event had occurred. And he told me about other email evidence that supports the fact that it didn't happen," said Falwell, whose father, the Rev. Jerry Falwell, founded Liberty University in the 1970s and was a driving force in the "religious right" of that era.

The college president said if the alleged acts had occurred, he believes the women would have sued the wealthy businessman.

"Donald Trump's a billionaire. If this had happened, I have no doubt in my mind that the accusers would have brought suits many years ago," Falwell said.

Trump said Thursday that he will soon release evidence showing that the most recent accusations are false.

"We already have substantial evidence to dispute these lies and it will be made public in an appropriate way and at an appropriate time very soon," he said at a rally in West Palm Beach, Florida. "These lies come from outlets whose past stories and past claims have already been discredited."

"These people are horrible people. They're horrible, horrible liars," Trump added.

The nominee accused the Times of ignoring proof Trump's team presented showing holes in Leeds' story.

"This weekend The New York Times published a full-page hit piece with another claim from an individual who has been totally discredited based on the many many emails and letters she has sent to our office over the years looking for work," he said.

Trump said the emails show Leeds wanting to attend his rallies and calling the businessman "great."

"But The New York Times refused to use the evidence that we presented," he said. "If they used it, they would have looked, they would have said 'There's no story here.'"

Early Thursday morning, a lawyer representing Trump, Marc E. Kasowitz, sent a letter to the Times saying "your article is reckless, defamatory and constitutes libel per se."

"We hereby demand that you immediately cease any further publication of this article, remove it from your website and issue a full and immediate retraction and apology. Failure to do so will leave my client with no option but to purse all available actions and remedies," he wrote.

Late Wednesday night, People Magazine also published a story where Natasha Stoynoff, a writer for the magazine, alleges that she had been physically attacked by Trump at Mar-a-Lago while. She was at the Florida mansion to write a profile on Trump's one-year wedding anniversary to his wife Melania.

The Trump campaign did not respond to request for comment regarding that story, but a Trump spokesperson told People, "This never happened. There is no merit or veracity to this fabricated story."

In a statement on the Times' report earlier on Wednesday night, Trump spokesman Jason Miller said the "entire article is fiction."

"For the New York Times to launch a completely false, coordinated character assassination against Mr. Trump on a topic like this is dangerous," Miller said in the 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."

"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," his statement continued.

More than 200 Liberty students are protesting Falwell's support of Trump, saying that the Republican presidential nominee "is actively promoting the very things that we as Christians ought to oppose."

The letter said that if any Liberty University faculty or staff member had made the comments Trump made on the tape, they would have been terminated.

"Because our president has lead the world to believe that Liberty University supports Donald Trump, we students must take it upon ourselves to make clear that Donald Trump is absolutely opposed to what we believe, and does not have our support," the letter states.

But Falwell told CNN's John Berman that the number of students who signed the letter is overstated.

"We do have a small group of the 'Never Trump' crowd on campus, who would rather see Hillary elected than Donald Trump," he said. "I received many, many tweets and messages from people who say, 'I signed it and I'm not a student. I'm an alumni or I'm not affiliated with Liberty at all."

Falwell also said the petition falsely presents how he has advocated for Trump.

"Some of the things they said in that statement are not true," he added. "I've always been careful to make it clear that my endorsement of Trump is mine only. I'm not speaking for the university."