Republican presidential frontrunner Donald Trump has denied he was mocking a New York Times reporter by jerking his arms around, saying he had no idea what the journalist looked like when he imitated him during a rally in South Carolina this week.

In a statement late Thursday, Trump said the reporter, Serge Kovaleski, who has a congenital condition that limits joint mobility, "should stop using his disability to grandstand." Two days earlier, at the South Carolina rally, the billionaire real-estate tycoon and former reality-TV star spoke about the reporter while flailing his arms around. "Poor guy, you oughta see this guy," Trump said, slurring his words in a poor imitation of Kovaleski.

The candidate 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 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.

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."

"Despite having one of the all-time great memories, I certainly do not remember him," he added.

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.

This week, Kovaleski told CNN he did not recall the events in New Jersey on 9/11 as told by Trump.

"We did a lot of shoe leather reporting in and around Jersey City and talked to a lot of residents and officials for the broader story," Kovaleski said on CNN. "Much of that has, indeed, faded from memory.

"I do not recall anyone saying there were thousands, or even hundreds, of people celebrating. That was not the case, as best as I can remember."

Since announcing his candidacy for the 2016 presidential elections, Trump has had numerous public scraps with the media, which has been frustrated by the candidate's attempts to restrict reporters' access to his events, control the length and substance of live debates, and even revoke press credentials.

Trump's campaign staff has threatened to blacklist journalists if they dare step out of the specially-designated area for members of the media during campaign events. Last week, Trump's campaign manager, Corey Lewandowski, hassled CNN reporter Noah Gray at an event in Massachusetts, ordering him to get back "inside the pen or I pull your credentials." Lewandowski then reportedly told Trump's spokesperson, Hope Hicks, "Tell Noah, Get back in the pen or he's fucking blacklisted," according to a recording cited by the Washington __Post.

A day later, a Buzzfeed reporter also said he was banned from a Trump event in Iowa.