JERSEY CITY, N.J. (CBSNewYork/AP) — The leader of a national Muslim-American organization has invited Republican presidential candidate Donald Trump to come to Jersey City and meet with Muslims there.

Last month, Trump claimed he saw television reports of “thousands of people” in Jersey City cheering as the Twin Towers fell on Sept. 11, 2001. The city has a significant population of Muslim immigrants. There is no evidence of that actually having happened.

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Trump also has said he would use a database to track Muslims in the U.S. if he’s elected.

Jersey City Mayor Steven Fulop said they searched 911 phone records and police reports, and there’s “nothing to substantiate at anytime that that actually happened.”

At a news conference in Jersey City on Thursday, Nihad Awad of the Council on American-Islamic Relations called Trump’s comments “vicious and unfounded” and invited him to visit the city.

“Donald Trump and his reckless statements is putting the lives of millions of Americans and their families in danger,” Awad  said. “This is a time of unity and we have to reject any attempt to marginalize any minority in our nation if we have learned anything from our history.”

Awad also spoke on Wednesday’s mass shooting in San Bernardino, Calif.

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“We are heartbroken and horrified,” Awad said. “We stand firm as one community in condemning this attack.”

He hopes people won’t jump to conclusions about the attacks because the shooters were Muslim.

“I do not know of any religion that condones or justifies the killing of innocent people,” Awad said.

CAIR-NJ Board Chair Nadia Kahf said she fears there will be an unfair backlash against Muslims. She blames divisive rhetoric and named Trump as the main culprit in demonizing Muslims, WCBS 880’s Levon Putney reported. She noted in coverage of the recent Planned Parenthood shooting in Colorado, even though the shooter was Christian “you don’t identify those individuals as terrorists.”

A spokeswoman for Trump’s campaign didn’t immediately respond to an email seeking comment.

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