Trump is riding a new high in the polls as a result, but critics say he's manipulating voters and distorting the truth.
"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," he said.
In the chaos after 9/11, there were some false reports and internet rumors, but despite being widely debunked, Trump insists he saw it and stood by his comments on "This Week" with George Stephanopoulos.
"It did happen, I saw it," Trump said. "It was on television, I saw it...It did happen."
According to the latest ABC News/Washington Post poll, terrorism has surged as an election issue since the Paris attacks, and Trump leads with a wide margin as the most trusted to deal with the issue among Republican voters.
But Jersey City's current mayor says Trump is perpetuating a falsehood.
"Either he's willfully making up lies or he has memory issues," Mayor Steven Fulop said. "And if you have either one of those, you have to question his ability to be president."
But Trump isn't backing down on this or some other claims, including retweeting false statistics about crime whose source appears to be a white supremacist group. The tweet showed a dark-skinned man with a gun and various stats suggesting many murder rates are driven by African Americans. It claimed 16 percent of white people murdered are killed by other whites, while 81 percent of white people murdered are killed by blacks.
The FBI's 2014 report on U.S. homicides shows 82 percent of whites who are murdered are killed by other whites. Blacks were actually responsible for 15 percent of white murders.