Story highlights Cohen said the argument over numbers of people celebrating is misplaced, and that Trump was making a broader point about enemies within the U.S.

The Trump aide also issued a warning to the Republican Party over trying to go after real estate mogul

Washington (CNN) Donald Trump and his camp are standing behind disputed claims the presidential candidate made about people in New Jersey celebrating after the 9/11 attacks, with a top aide saying Tuesday that the mogul is "probably right" about what happened.

Trump over the weekend and through Monday repeatedly said that he saw on TV American Muslims in New Jersey celebrating on Sept. 11, 2001, as the Twin Towers fell, a claim that fact-checking publications have called false. Though there were some reports of celebrations investigated by police, there is no record of any such footage being aired on television or anything to suggest "thousands" celebrated, as Trump suggested.

On Tuesday, Trump's chief counsel, Michael Cohen, stood by the comments, even as he was pressed by CNN's Chris Cuomo on the fact that there's no evidence to back up the claims and that accuracy matters in a presidential race.

"He's probably right," Cohen said of Trump on "New Day." "There's no way to say that it wasn't."

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