By Erin McPike

WASHINGTON (Reuters) - Republican presidential candidate Donald Trump on Saturday reframed his claim that he saw Muslims in Jersey City, New Jersey, cheering the attacks on the Twin Towers of the World Trade Center in Manhattan on Sept. 11, 2001 by asserting the sentiment was shared worldwide.

“Worldwide, the Muslims were absolutely going wild,” the real estate mogul said at a campaign rally in Sarasota, Florida.

Trump came under fire a week ago for saying at another rally and in a nationally televised appearance that he watched thousands of people in Jersey City cheer the World Trade Center’s implosion. Fact checkers debunked his claim.

Still, 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. Trump has been among the most vocal of the Republican candidates in raising skepticism 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 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 percent to 31 percent, although he continues to hold a wide lead over his competitors.

Trump used ample time in his remarks to point out how far ahead he is in opinion polling in many states, and he defended his recent commentary.

To back up his claims of seeing spectators celebrate 9/11, this week 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 Trump cited his article that he has no recollection of his reporting producing evidence of hundreds or thousands of people celebrating.

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In his speech, 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,” Trump told the cheering crowd. “I’m telling you, I would never do it.”

With reports mounting of 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?”

(This story corrects paragraph 7 to make clear the article mentioned alleged celebrations but the allegations were not corroborated; deletes reference to the article being corrected; inserts a sentence in paragraph 8 about Kovaleski's comments this week)

(Reporting by Erin McPike; Editing by Dan Grebler and Frances Kerry)