ROCK HILL, SC -- As GOP candidate Donald Trump doubles down on claims that he saw Americans in New Jersey cheering on 9/11, his rival, Jeb Bush strongly denounced those comments today while campaigning in South Carolina.

"I don’t recall that. There was no cheering on any -- it would have been television, it would have been recorded.”

A memory he said he instead recalls is that of peaceful Muslim-Americans.

“What I remember were a lot of peaceful Muslims that were disheartened and grieved and sad and angry just as every other American was as well,” he said.

Trump defended comments he made Saturday -- that he saw thousands of people in Jersey City, New Jersey cheering when the World Trade Center was destroyed on Sept. 11, 2001.

"There were people that were cheering on the other side of New Jersey where you have large Arab populations,” he told George Stephanopoulos today on ABC’s “This Week.” "They were cheering as the World Trade Center came down. I know it might be not politically correct for you to talk about it, 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.”

These claims have been widely debunked. ABC News, among many other news organizations has investigated and no evidence of such cheering in Jersey City has been found.

While there were images of people cheering the towers’ collapse in parts of the Middle East, there is no record of such celebrations in New Jersey. There were some Internet rumors of Muslims celebrating the towers’ fall in Paterson, New Jersey, but those were discounted by local police at the time.

Jordyn Phelps contributed to this report.