Republican presidential candidate Donald Trump denied on Thursday he was mocking the physical disability of a New York Times reporter during a campaign speech in which he flailed his arms and distorted his speech in an imitation of the journalist.

The latest uproar over Trump's behavior on the campaign trail was ignited by remarks the billionaire real-estate tycoon and former reality-TV star made during a South Carolina rally on Tuesday about the Sept. 11, 2001 attacks on New York's World Trade Center.

Trump, front-runner for his party's nomination for the November, 2016 election, was defending his unsubstantiated assertions that thousands of Muslims were seen in New Jersey cheering the collapse of the Twin Towers. During the speech, he singled out Times investigative reporter Serge Kovaleski for a story he wrote a few days after the attacks while he was then a Washington Post correspondent.

That article reported authorities had detained "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 accounts have never been authenticated.

Kovaleski himself said in a recent CNN interview that he did "not recall anyone saying there were thousands, or even hundreds of people celebrating. That was not the case, as best I can remember."

While not referring to Kovaleski by name in his speech, Trump accused the reporter of backing down from his own story.

"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 at the microphone, jerking his arms in front of his body and slurring his words in a crude impression of the reporter.

Kovaleski suffers from a congenital condition called arthrogryposis, which limits mobility and muscle development in the joints.

The New York Times issued a statement on Thursday rebuking Trump, saying, "We think it's outrageous that he would ridicule the appearance of one of our reporters."

Trump fired back on social media, denying he had made fun of Kovaleski's disability or would even recognize him.

"I merely mimicked what I thought would be a flustered reporter trying to get out of a statement he made long ago," Trump wrote. "If Mr. Kovaleski is handicapped, I would not know because I do not know what he looks like. If I did know, I would definitely not say anything about his appearance."

He also accused Kovaleski of "using his disability to grandstand."

In an interview for the Times, Kovaleski said he was certain Trump remembers him from his days covering the real estate developer for the New York Daily News in the 1980s, and that the two were "on a first-name basis for years."

"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," the Washington Post quoted him saying in a separate interview.