He later repeated his claim to ABC News host George Stephanopoulos, adding that the cheers came from areas of New Jersey with “large Arab populations”.
The claims were denied by Jersey City Mayor Steven Fulop and police.
Fifteen of the 19 hijackers on 9/11 were citizens of Saudi Arabia - a country omitted from the list of countries included in his controversial travel ban.
In an interview about his first 100 days in the White House with the Associated Press, Donald Trump boasted that his “ratings” on cable network shows like on Fox and CBS’ Face the Nation were higher than those for broadcasts of the 9/11 terrorist attacks.
And George Bush — by the way, George Bush had the chance, also, and he didn't listen to the advice of his CIA." Mr Trump insisted he knew many of the people working in the Twin Towers, but never named a single person.
The President would have had to have known about one in 10 of the victims if his claim of knowing “hundreds” of the 2,996 victim was true.
Within hours of his inauguration, he punished the National Park Service for posting pictures of his ceremony which seemed to compare his crowds with a much higher turnout for Barack Obama.
The money had originally been set aside for small businesses in the area.
The then-presidential candidate said at a rally in Birmingham, Alabama, that people had celebrated the disaster across the water from the Twin Towers.
And as Mr Trump readies himself for the first 9/11 commemoration as President, the litany of controversial remarks will come under fresh scrutiny.
This time last year, the footage of his former rival Hillary Clinton buckling at the knees and being helped into a vehicle, sparked a vicious debate about her health and fitness for office.
Some are funny, others are sentimental, but all will make you think.