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Story highlights

Former New York Mayor Rudy Giuliani said Donald Trump is "exaggerating" when he claims that thousands of Muslims cheered on 9/11

Giuliani said it was now Trump's responsibility to provide evidence of the cheering

(CNN) —  

Former New York Mayor Rudy Giuliani said Tuesday that while there was some celebrating by American Muslims in New York on Sept. 11, 2001, Donald Trump is “exaggerating” when he said thousands of Muslims were cheering the attacks.

“We did have some celebrating, that is true,” Giuliani told CNN’s Alisyn Camerota on CNN’s “New Day.” “We had pockets of celebration some in Queens, some in Brooklyn – 10, 12, 30, 40” people.

Giuliani recounted hearing about a Muslim-owned candy store where some Muslims were cheering the attacks and were beaten up by children from a neighboring housing development.

RELATED: Trump on Muslim claim: ‘I’m not going to take it back’

But Trump’s characterization, that thousands were celebrating the attacks, is wrong and it’s up to Trump to show his evidence, Giuliani said.

“I don’t want to say he’s not telling the truth or not. Let him deal with it. Let him explain to people. Let him show the evidence of it,” Giuliani said. “If thousands of people were demonstrating and he saw it on television, then there must be some tape of it somewhere. If it shows up it will corroborate him. If it doesn’t show up it’s going to make him look really bad.”

Other local politicians and several media outlets have sharply disputed Trump’s claim of “thousands” of American Muslims celebrating, including Politifact, which rated the charge “pants on fire” and The Washington Post, which rated it “four Pinocchios.”

Neither outlet could find any specific evidence to corroborate Trump’s allegation, though there were a handful of reports of rumors that there were celebrations in New Jersey, along with images of Palestinians celebrating overseas.

A September 17, 2001, Associated Press story referred to “unfounded … rumors of rooftop celebrations of the attack by Muslims” in Jersey City, New Jersey.

And a September 18, 2001, story from The Washington Post 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.”

RELATED: Carson walks back support for Trump’s disputed 9/11 celebration claim

CNN’s Tal Kopan contributed to this report.