Donald Trump has defended his declaration that he saw thousands of Muslims in Jersey City celebrate the 9/11 terror attacks.

The presidential candidate, who is considered the Republican frontrunner for the 2016 election, said he was "100 per cent right" when he made the comments at a rally and on television earlier this month. He says he recalls televised footage of Muslims celebrating the collapse of the World Trade Centre and an attack on the Pentagon that resulted in the deaths of almost 3,000 people. However, fact-checkers have said no such celebrations took place.

"I saw it. So many people saw it. And, so, why would I take it back? I'm not going to take it back," Trump told NBC on Sunday. He said he's heard from "hundreds" of people who say they also remember the footage.

"All over the world – forget about New Jersey for a second – all over the world, it was reported that Muslims were celebrating the fall of the World Trade Centre," he continued.

"It did happen in New Jersey. I have hundreds of people that agree with me.

"I have a very good memory, I'll tell you. I saw it somewhere on television many years ago. And I never forgot it."

A number of public officials have disputed Trump's claims, including fellow Republican candidate New Jersey Governor Chris Christie, who said: "I think if it had happened, I would remember it."

Trump has come under fire for his comments, which follow a number of statements about Muslims that have been widely deemed offensive and dangerous.

In the wake of the Paris terror attacks he said he would consider the surveillance of mosques, and that he would "certainly implement" a database of American Muslims.

An open letter written to Trump by a young Muslim woman in California went viral when she condemned his remarks.

"I heard you wanted us to start wearing ID badges, so I decided to choose one for myself. I am not easily identifiable as a #Muslim just by looking at me, so my new badge will let me display proudly who I am. I chose the peace sign because it represents my #Islam," 22-year-old Marwa Balkar wrote in a Facebook post which has now been shared over 160,000 times.

"I heard you want to track us as well. Great! You can come with me on my Cancer Awareness walks at the local middle school, or you can follow me to work where it's my job to create happiness. You can also see how my local mosque makes PB&J sandwiches for the homeless and hosts interfaith dinners where everyone is welcome.

"Maybe then you'll see that me being Muslim doesn't make me any less American than you are. Maybe if you walk in my footsteps, you can see that I am not any less human than you are. Salaamu alaikum ✌? ‪#‎NOTINMYNAME‬‪#‎FightWithPeace‬".