GOP Presidential front-runner Donald Trump is refusing to back down on the controversial claim he made Saturday that he saw "thousands" of people in Jersey City, N.J., celebrating "when the World Trade Center came tumbling down" on Sept. 11, 2001.

Trump first recounted the story at a rally in Birmingham, Ala., as he emphasized the need for enhanced surveillance, including monitoring specific mosques, as well as stronger border security, in the wake of the Paris attacks, according to FOX News.

"I watched when the World Trade Center came tumbling down. And I watched in Jersey City, New Jersey, where thousands and thousands of people were cheering as that building was coming down," Trump said.

Trump then appeared on ABC's "This Week" on Sunday where he repeated the claim after host George Stephanopoulos argued that police had already refuted such rumors, according to Media Matters.

"It did happen. I saw it," said Trump. "It was on television. I saw it."

"There were people that were cheering on the other side of New Jersey, where you have large Arab populations. They were cheering as the World Trade Center came down," he said. 

"I know it might be not politically correct for you to talk about it," he added, "but there were people cheering as that building came down, as those buildings came down. And that tells you something. It was well covered at the time."

Jersey City Mayor Steven Fulop, in response to Trump's accusations, criticized him, saying that Trump "has memory issues or willfully distorts the truth, either of which should be concerning for the Republican Party." 

"Trump is plain wrong, and he is shamefully politicizing an emotionally charged issue. No one in Jersey City cheered on September 11th," Fulop said, according to ABC News. "We were actually among the first to provide responders to help in lower Manhattan. Trump needs to understand that Jersey City will not be part of his hate campaign."

Footage of Muslims in the Middle Eastern countries cheering news of the attacks were often broadcast on television shortly after 9/11, but there is no evidence in news archives of mass celebrations by Muslims in Jersey city.