Has Donald Trump gone too far this time?

The Republican presidential hopeful is under fire for mocking a New York Times reporter with an 'outrageous' impression of the journalist's physical handicap during a campaign speech on Wednesday.

Not only has the New York Times come to the defense of their reporter, Serge Kovaleski, but the journalist's colleagues and the public at large have taken to social media to register their disgust with the brash candidate.

'Donald Trump making fun of a handicapped reporter. How sorry can one get. This guy wants to be president? What a joke!' one Twitter user named Richard Kirby wrote on Thursday.

Meanwhile, Trump has refused to back down from his mockery and has even demanded an apology from the Times.

He released a statement on Thanksgiving afternoon, saying: 'Serge 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.

'He should stop using his disability to grandstand and get back to reporting for a paper that is rapidly going down the tubes.'

Scroll down for video and Trump's full statement on the scandal

Donald Trump has come under fire for an 'outrageous' impression of a disabled New York Times reporter

The Republican presidential candidate mocked esteemed journalist Serge Kovaleski, who suffers from a chronic condition which effects the movement in his arms

Trump laid into Kovaleski (right), doing an impression that saw him flail his limp arms around his head while putting on a strange voice

Trump has been at odds with Kovaleski, ever since the real estate mogul controversially claimed 'thousands of thousands' of Arabs were celebrating in the streets of New Jersey after the 9/11 attacks.

When Trump's claims were debunked, he said he had based his statements on an article Kovaleski wrote fourteen years ago for the Washington Post.

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However, Kovaleski said that he wrote reports of 'a number of people... allegedly' celebrating in New Jersey, but that he never actually saw these revelers and that he has no idea where Trump got his figure from.

Instead of admitting he had got it wrong, Trump went on the offensive against Kovaleski on Wednesday, mocking the reporter's physical condition that impacts his ability to move his arms.

In a campaign stop in Myrtle Beach, South Carolina, Trump laid into the journalist, doing an impression that saw him flail his arms while putting on a strange voice.

Before the distasteful imitation, Trump said the story was 'written by a nice reporter'.

But he continued: 'Now the poor guy, you gotta see this guy: "Uh, I don’t know what I said. I don’t remember." He’s going, "I don’t remember. Maybe that’s what I said."'

Kovaleski, a Pulitzer Prize-winning journalist, was born with arthrogryposis.

The condition can cause sufferers' joints to get stuck in one position and can also see people born with weaker or missing muscles.

When Trump started to receive backlash from the imitation, he issued a statement saying he had 'no idea who 'Serge 'Kovalski' (notably spelling his last name wrong) is, despite the fact that the reporter covered Trump when he worked at the New York Daily News. Trump claims to have 'one of the all-time great memories'.

Trump said: 'His recent statement, to me, 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 my speech before over 10,000 people in Myrtle Beach, SC, I merely mimicked what I thought would be a flustered reporter trying to get out of a statement he made long ago.

'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.'

Trump went on to claim he has spent tens of millions of dollars making sure his buildings are handicap accessible.

He then attacked the New York Times for 'trying to make a story of of nothing' while also refusing to back down from his heavily refuted claims.

'Over the last number of days, since this issue arose, I have received many phone calls and tweets from people that said I was right about Muslims in New Jersey celebrating the fall of the World Trade Center. Throughout the world it was openly celebrated and so reported,' Trump claimed.

Kovaleski, a Pulitzer Prize-winning journalist wrote an article in 2001 that said police questioned a number of people allegedly celebrating 9/11 attacks

Unreliable source: Trump tweeted an array of articles he claims support his view, including one by conspiracy theory website Infowars

Trump took to Twitter to blast the New York Times for taking 'constant hits' at him in what was a thinly-veiled swipe at their response to his impression

Sources in the campaign, speaking anonymously, previously told the Washington Post that Trump was 'not aware of any condition and was not mocking his physical appearance in any way'.

Kovaleski said he is certain the candidate remembers him and his condition.

'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,' Kovaleski told the Post .

A spokeswoman for the Times said: 'We think it's outrageous that he would ridicule the appearance of one of our reporters.'

Kovaleski's colleagues at other publications also jumped to his defense.

ESPN reporter Don Van Natta JR tweeted that Kovaleski 'is one of the best reporters - and best people- that I know' and called Trump's impression 'despicable'.

Times reporter Dan Barry tweeted: 'The measure of men. Know this: Serge Kovaleski ... is a journalistic rock star and one great colleague.'

The Ruderman Family Foundation offered Trump sensitivity training sessions to help him better understand people with disabilities.

A petition calling on the Republican front-runner to apologize has also been circulating online.

Kovaleski, a Pulitzer Prize-winning journalist who now works for the New York Times, was born with arthrogryposis, which affects the movement of his arms

That prospect looks somewhat unlikely, however, with Trump taking to Twitter to blast the New York Times for taking 'constant hits' at him in what was a thinly veiled swipe at their response to his impression.

He wrote: 'The failing @nytimes should be focused on good reporting and the papers financial survival and not with constant hits on Donald Trump!'

Trump also tweeted an array of articles he claims support his view that there were thousands of Arabs celebrating the September 11 attacks in New Jersey.

However among these was a link to conspiracy theory website Infowars, which is run by Alex Jones - known for his bizarre statements on 9/11 and the moon landings.

The person who wrote the article claims they saw 'a pocket' of people in 'traditional Muslim garb dancing, jumping, shouting and celebrating like their team had won the Super Bowl, just as Trump said'.

There is no evidence to substantiate the claim.

Back in 2001, a week after the attacks, Kovaleski wrote: '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.'

He told CNN this week: 'I do not recall anyone saying there were thousands, or even hundreds, of people celebrating.'

Trump said last week during a campaign stop in Birmingham, Alabama, that he saw 'thousands of people cheering' as the World Trade Center collapsed.

He repeated his claims on ABC on Sunday, saying: 'There were people that were cheering on the other side of New Jersey, where you have large Arab populations. They were cheering as the World Trade Center came down.'