According to Donald Trump, the Republican Party’s front-runner for its presidential nomination, there was a massive public celebration in Jersey City as the Twin Towers imploded on September 11, 2001.

“I watched when the World Trade Center came tumbling down,” he was reported as having said on Saturday, at an event in Birmingham, Ala. “And I watched in Jersey City, New Jersey, where thousands and thousands of people were cheering as that building was coming down.”

“That never happened,” Steven Fulop, Jersey City’s mayor, said.

Although Mr. Trump later clarified that he was not in Jersey City on September 11, despite having implied at first that he had been, he refused to back down from the rest of his assertion. But, Mayor Fulop said, there was no television broadcast of something that did not happen.

“When you look at the media outlets, there isn’t one that substantiates what he said,” Mr. Fulop said. “There is not footage of it, and there are no reports.”

The original rumor — which set the public jubilation over the deaths of thousands of people in Paterson, not Jersey City — was “an urban legend, fueled by anti-Muslim sentiment, and Trump is looking to capitalize on it,” Mr. Fulop continued.

He resents it.

Steve Fulop

Steve Fulop

“We in Jersey City do not appreciate it. We have done a lot of work to create a community that is diverse, where everyone works together. We do Muslim events, we do Jewish events. Jersey City is a city that speaks to a lot of American culture on diversity. So for him to single us out as an example of hatred…” His voice trailed off.

“It certainly evoked a response from people here, though,” he resumed. “People resent what he said. The silver lining is that I believe that a campaign of hate will not win in the general election. If he is the nominee for the Republican side, the end result will be a Democratic president.

“Which works for me,” added Mr. Fulop, who is a Democrat.

Mr. Trump did evoke a response from Jersey City residents. “A lot of people in the Muslim community reached out” in support of their city and in outrage over Mr. Trump’s comments, Mr. Fulop said.

Jersey City is right across the Hudson from the World Trade Center, and the attack, clearly visible across the river, spurred many people there into action. “Jersey City first responders helped out in lower Manhattan,” Mr. Fulop said. “Jersey City’s trauma center was set up to help victims, and Liberty State Park was used as a staging center. Thousands of people volunteered.”

The Jewish Standard’s coverage of those nightmare weeks shows no evidence of street celebrations over the carnage anywhere in the United States, although we did report in passing on the rumors from Paterson, which we pointedly said that no one could source, much less prove. On September 28, a long story looked at reactions in Jersey City. We quoted three local rabbis — Orthodox, Conservative, and Reform — none of whom mentioned anything about street celebrations. Each one instead talked about the profound shock, deep sadness, urge to help, and feeling of community the city shared.

For Mr. Fulop, there is some irony in Mr. Trump’s attack on Jersey City. Mr. Fulop, who is Jewish, the grandson of Holocaust survivors, had moved to Jersey City in 2000. He was not politically active then. He worked for Goldman Sachs at 1 New York Plaza in lower Manhattan. On September 11, at work there, “I felt the building shake when the planes hit,” he told us last year. It shook him in every possible way. “Soon I started talking to recruiters,” he said; it wasn’t long before he was in uniform. A Marine uniform. After boot camp at Parris Island, he served in Iraq.

“Jersey City is a big city,” he said; it is the state’s second largest, with a population of more than 262,000 people reported in 2014. “So I am sure that there are some people here who harbor a hatred for the country. But to say that there were thousands of people who were dancing in the streets — it is a tall tale.

“It is Trump having a vivid imagination. And at some time I hope that the public calls him out on it. But he has crossed the line so many times, and no one does call him out on it.”

And then he returned to the silver lining. “There is one thing that might come out of it. The Jersey City community will come closer together, and we will continue to move together, working together to build one of the most diverse communities in the country.”