Republican presidential candidate Donald Trump has reframed his claim that he saw Muslims in New Jersey cheering the September 11 attacks by asserting the sentiment was shared worldwide.

Mr Trump came under fire a week ago for saying he watched thousands of people in Jersey City cheer the World Trade Centre’s implosion. Fact checkers debunked his claim.

At a campaign rally in Sarasota, Florida, on Saturday (local time), Mr Trump instead said: “Worldwide, the Muslims were absolutely going wild.”

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To back up his claims of seeing spectators celebrate 9/11, Mr Trump cited a 2001 Washington Post article that mentioned authorities detaining a number of people in Jersey City who had allegedly celebrated the attack on rooftops with views of the site.

The article was written by Serge Kovaleski, who has a disability and now writes for the New York Times.

The Post article did not say the authorities’ allegations had been corroborated and Kovaleski has said in interviews since Mr Trump cited his article that he has no recollection of his reporting producing evidence of hundreds or thousands of people celebrating.

In his speech, Mr Trump sought to distance himself from appearing to have mocked the reporter during an event Tuesday night.

“I would never mock a person that has a disability,” he told the cheering crowd.

“I’m telling you, I would never do it.”

Trump a vocal sceptic of Muslims living in the US

Mr Trump has been among the most vocal of the Republican candidates in raising scepticism about Muslims living in the United States.

When prompted by a reporter, he said he would not oppose creating a national database that tracks Muslims in the country.

The controversial remarks may be taking a toll on Mr Trump, who has seen his support in Reuters/Ipsos opinion polling of Republican voters nationally take a sharp downturn in the past week.

In the past five days, he dropped 12 points from 43 per cent to 31 per cent, although he continues to hold a wide lead over his competitors.

With reports mounting of Mr Trump’s rallies growing rough, the candidate urged his audience to be polite to a heckler who briefly brought the Sarasota event to a halt.

“Be nice to the person. Don’t hurt the person,” he instructed the crowd, which cheered him loudly when he told security personnel to escort the heckler from the room.

“Do you see how diplomatic I’ve become?”

The race ahead of the November 2016 presidential election has taken a sharp turn toward focusing on terrorism in the aftermath of the attacks in Paris two weeks ago.