At a rally in Myrtle Beach, S.C., on Nov. 24, 2015, Republican presidential candidate Donald Trump talks about New York Times reporter Serge Kovaleski . (Reuters)

A day after he was widely rebuked for mocking a reporter with a physical disability, business mogul and reality TV star Donald Trump on Thursday denied that he had done so and accused the reporter of “using his disability to grandstand.”

Trump also demanded an apology from the New York Times, the reporter’s employer, which earlier in the week issued a statement condemning Trump for ridiculing “the appearance of one of our reporters.”

The incident occurred Tuesday at a rally in South Carolina, as Trump was defending his recent claim that he had witnessed thousands of Muslims cheering in New Jersey on Sept. 11, 2001, as the World Trade Center towers collapsed. On stage, Trump berated Times investigative reporter Serge Kovaleski for his recent recollection of an article he wrote a few days after the attacks, which Trump has been citing to defend his claim.

Trump appeared to mock Kovaleski’s physical condition; the reporter has arthrogryposis, which visibly limits flexibility in his arms.

“Now, the poor guy — you’ve got to see this guy, ‘Ah, I don’t know what I said! I don’t remember!’ ” Trump said as he jerked his arms in front of his body.

Trump’s assertions about Muslims celebrating in 2001 have been fact-checked and discredited by law enforcement and government officials who were in New Jersey in the days and weeks after the terrorist attacks.

Trump has defended his recollections by citing a 2001 article by Kovaleski, who worked for The Washington Post at the time and wrote that “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.”

Those allegations were never corroborated but have persisted in online rumors in the 14 years since the attacks. In an interview on CNN this week, Kovaleski said he did not recall “anyone saying there were thousands, or even hundreds, of people celebrating.”

That is the statement that apparently drew Trump’s ire on Tuesday.

“The sad part about it is, it didn’t in the slightest bit jar or surprise me that Donald Trump would do something this low-rent, given his track record,” said Kovaleski, who frequently covered Trump while reporting for the New York Daily News between 1987 and 1993.

In a statement Thursday, Trump adamantly denied that his comments or gestures were meant to mock Kovaleski. He also denied remembering Kovaleski at all — “despite having one of the all-time great memories.”

“Kovaleski must think a lot of himself if he thinks I remember him from decades ago — if I ever met him at all, which I doubt I did,” Trump said. “He should stop using his disability to grandstand and get back to reporting for a paper that is rapidly going down the tubes.”

Serge Kovaleski on April 21, 2010, in New York. (Neilson Barnard/Getty Images)

Kovaleski said in an interview this week that he’s sure Trump remembers him — and his disability. Trump indicated as much himself in the speech Tuesday, when he said, before he began an apparent impersonation with a series of jerking arm movements, that the article had been “written by a nice reporter.”

In his statement Thursday, Trump said: “I have no idea who this reporter, Serge Kovalski [sic] is, what he looks like or his level of intelligence. I don’t know if he is J.J. Watt or Muhammad Ali in his prime — or somebody of less athletic or physical ability. Despite having one of the all-time great memories I certainly do not remember him.”

Trump added that he thought Kovaleski’s recollections about his 2001 article “seemed like (again without knowing what he looks like) he was groveling and searching for a way out from what he wrote many years before.”

In Kovaleski’s comments to CNN and other news organizations, the reporter pointed out that there were never any reports of thousands or even hundreds of Muslims celebrating, as Trump has claimed to have witnessed. Kovaleski has not contradicted the 14-year-old article.

Kovaleski’s friends and colleagues took to social media this week to excoriate Trump.

“The measure of men. Know this: Serge Kovaleski, aka @sergenyt, is a journalistic rock star and one great colleague,” Times reporter Dan Barry wrote on Twitter.

“@sergenyt is one of the best reporters — and best people— I know. This is despicable,” ESPN reporter and author Don Van Natta Jr. wrote.

Trump took specific aim at the Times in his statement Thursday.

“They should focus on the survival of their newspaper and not on dishonest and very bad reporting about me,” he said. “The New York Times has become more and more irrelevant and rapidly becoming a total joke — sad!”

A Times representative declined Thursday to add to the paper’s earlier statement.