At a rally in South Carolina Tuesday, when GOP frontrunner Donald Trump was defending the contention that "thousands and thousands of people" cheered the September 11th terrorist attack in Jersey City, New Jersey, he did an impression of a reporter's physical handicap.

The reporter was Serge Kovaleski, who had, according to Politico, previously covered Trump when he worked for the New York Daily News. He also helped write a September 2001 Washington Post story that Trump has been using to back up his claim about what he saw at the attacks.

"Written by a nice reporter. Now the poor guy. You ought to see this guy," Trump said.

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When he made fun of Kovaleski verbally, Politico reported, he launched "into an impression which involved gyrating his arms wildly and imitating the unusual angle at which Kovaleski's hand sometimes rests."

Kovaleski suffers from arthrogryposis, which according to the National Institutes of Health, can impact the function and range of motion of joints and can cause muscles to atrophy. Kovaleski was familiar to Trump because he had, according to Politico, covered Trump for several years when he worked for the New York Daily News.

Trump described the 2001 Washington Post story to the audience like this: "It says in Jersey City, within hours of two jet liners plowing into the World Trade center, law enforcement authorities detained and questioned a number of people who were allegedly seen celebrating the attack and holding tailgate style parties -- you know what tailgates are? That's like for football games. A lot of people on rooftops and also, by the way, on streets. On rooftops while they watched the devastation on the other side of the river."

The Post's story said that after the attacks, "Law enforcement authorities detained and questioned a number of people who were allegedly seen celebrating the attacks and holding tailgate-style parties on rooftops while they watched the devastation on the other side of the river."

The Washington Post's Glenn Kessler fact checked Trump's Jersey City account and found it to be false. One person he contacted during his reporting was Kovaleski, who told him, "I certainly do not remember anyone saying that thousands or even hundreds of people were celebrating."

Trump seemed to be aware of this and referred to this quote at the rally, when he said mockingly of Kovaleski's recollection of the story, "'Oh, I don't know what I said, ah, I don't remember!' He's going, 'Oh, I don't remember. Maybe that's what I said.'"

The New York Times, where Kovaleski is an investigative reporter and culture correspondent, on Wednesday released a statement to Politico, which first reported the incident. "We think it's outrageous that [Trump] would ridicule the appearance of one of our reporters," said a spokeswoman for the Times. CBS News has reached out Trump's campaign, but so far they have not commented further on the incident.

CBS News' Donald Judd contributed to this report