Donald Trump. REUTERS/Jay LaPrete In a Monday-night campaign speech, real-estate mogul Donald Trump doubled and tripled down on a claim widely disputed by fact-checkers.

The Republican presidential front-runner insists he saw "thousands of people" in Jersey City, New Jersey, celebrating the World Trade Center attack on September 11, 2001.

A wide swath of media fact-checkers reject that claim as completely unfounded, but Trump all but declared victory on the subject while speaking in Columbus, Ohio.

"I saw people getting together and in fairly large numbers celebrating as the World Trade Center was coming down, killing thousands of people," he said.

"The reporters are calling all day, all night. They want to find out: Did Trump make a mistake?" Trump recalled.

He added: "Believe me, it's being cleared off."

Trump repeatedly made the eyebrow-raising claim over the weekend while talking about the need to surveil certain mosques to prevent terrorism. Northern New Jersey has a large Muslim community.

Fact-checkers — including The New York Times, The Washington Post, PolitiFact, and others — reported that there is no basis to claim that "thousands and thousands" of people celebrated the September 11 attacks that day in New Jersey. However, the reports noted that footage exists of people celebrating the attacks in the Middle East, and that some evidence exists of much more limited celebrations in New Jersey.

Trump seized on one piece of that evidence during his Monday-night rally in Ohio: a September 18, 2001, Washington Post article stating that "law enforcement authorities detained and questioned a number of people who were allegedly seen celebrating the attacks and holding tailgate-style parties on rooftops" within hours of the attacks.

"'Tailgate,' you know what that means?" Trump asked his supporters. "That means: football games, Ohio State, thousands of people, in parking lots, on roofs. 'Tailgate' is a lot of people. 'Tailgate' is not two people."

The Post's own fact-checkers interviewed the reporters who wrote the September 18 story. Those reporters said they found no subsequent evidence to confirm the allegations they wrote about years ago.

But Trump predicted that The Post would back off the story, suggesting the newspaper would label it "a very long and winding typo."

He further assured NBC that he has the "world's greatest memory."

Donald Trump. Ty Wright/Getty Images

Trump also repeatedly said Monday that "hundreds of people" called his office to confirm his account of the people celebrating the September 11 attacks.

"I'm getting all of these tweets: 'I saw it.' 'I was there.' 'I was this,'" he recalled. "But I saw it. I saw it."

The Republican mogul also raised eyebrows on Monday by claiming he personally saw the people leaping to their deaths from the World Trade Center buildings.

"I watched people jumping off the building," Trump said. "Many people jumped. And I witnessed it. I watched that. Because I have a view — I have a window in my apartment that specifically was aimed at the World Trade Center. "

However, a CNN report subsequently questioned that claim by noting that he lived a healthy distance from lower Manhattan.

"The Republican presidential contender lives in Trump Tower in midtown Manhattan, more than four miles away from where the World Trade Center towers once stood," CNN's Jeremy Diamond wrote. "Trump has lived in the 5th Avenue tower since before the attacks, according to media reports pre-dating 9/11."