Donald Trump has signed the September 11 Victim Compensation Fund in the White House Rose Garden to fund the care of emergency workers who became ill after the terrorist attacks.

He also revived an old claim that he spent time at ground zero alongside firefighters and police officers.

Mr Trump has a long history of making questionable and provocative statements about what he saw on the day of the attacks and how he reacted, including some critical of Muslims.

At the signing ceremony, surrounded by emergency medical workers who had lost colleagues and friends in the attacks, the US president sought again to place himself near the centre of the recovery effort.

"Many of those affected were firefighters, police officers and other first responders," he said. "And I was down there also, but I’m not considering myself a first responder. But I was down there. I spent a lot of time down there with you.”

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According to Richard Alles, a retired deputy chief with the New York Fire Department, Mr Trump was not a presence at ground zero.

“I spent many months there myself, and I never witnessed him,” said Mr Alles, who was at the Rose Garden event. “He was a private citizen at the time. I don’t know what kind of role he could have possibly played.”

Mr Alles said he had vivid memories of meeting congresswoman Carolyn B Maloney, who became an integral part of passing the bill after the attacks. Ms Maloney did not attend the event at the White House earlier this week.

Mr Trump’s claims about where he was and what he was doing during the attacks date back years, with him often inserting and removing details along the way, Timothy O’Brien, the author of TrumpNation: The Art of Being the Donald, said.

“Donald Trump was absolutely not a first responder by any standard definition,” Mr O’Brien said. “If we’re defining it as the first wave of people who arrived at ground zero to provide help, he was not in that wave.”

On the day of the attack, Mr Trump called into WWOR-TV to say that he had a window in Trump Tower that looked directly over the World Trade Centre.

As the buildings burned, the show’s anchors praised his real estate prowess in a wide-ranging interview. Mr Trump said that if he had decided to run for president in 2000, he would have taken a “hard line” on the perpetrators, and that he had “somebody down there” near the attack who had witnessed at least 10 people jumping out of the World Trade Centre towers.

He also discussed a building he had in the area.

“40 Wall Street actually was the second-tallest building in downtown Manhattan and it was actually, before the World Trade Centre, was the tallest – and then, when they built the World Trade Centre, it became known as the second tallest,” Mr Trump said. “And now it’s the tallest.” (It was not.)

By the time Mr Trump hit the campaign trail in 2015, those initial stories had evolved into a mishmash of unproven claims.

Donald Trump jokes about stage collapsing as he invites 9/11 victims' families first responders up for bill signing

At a rally, he said he had watched people jump with his own eyes – possibly through a “solid gold” telescope – at Trump Tower. That claim is unproven, and Trump Tower is about 4 miles from the World Trade Centre site. He also shared another widely debunked claim that Muslims in New Jersey were celebrating after the planes hit.

In the days after the attack, Mr Trump ventured outside of Trump Tower to provide commentary, which largely focused on real estate and estimating the building costs of recovery.

In an interview with a German television station on 13 September, 2001, Mr Trump was asked if he would be personally involved in the recovery effort.

“I have a lot of men down here right now,” Mr Trump said. “We have over 100 and we have 125 coming. So we’ll have a couple of hundred people down here.”

He added: “We will be involved in some form helping to reconstruct.”

On 14 September, 2001, a Newsday report noted that Trump was in the vicinity of ground zero speaking on his mobile phone: “No, no. The building’s gone,” Mr Trump said over the phone.

A photo taken of him on 18 September, 2001, has been used in a widely circulated meme that claims Mr Trump personally travelled to ground zero with hundreds of workers to help uncover victims.

Mr O’Brien, the author, said the size of the Trump Organisation at the time was “a little bit over a dozen people,” which would have made it impossible to send hundreds of people to participate in the relief effort.

At the time, Mr Trump had a large number of casino workers based in Atlantic City, New Jersey, but there is no documented effort of him marshalling his resources to aid in the relief effort.

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“He’s very comfortable propagandising that event for political purposes,” Mr O’Brien said. “Even in the face of tragedy, he can’t help but self-promote and self-aggrandise.”

The donations Trump said he gave to charities involved in the relief effort are all unproven. In 2016, Scott M Stringer, the New York City comptroller, said there was no evidence that a $10,000 donation pledge that Mr Trump made after the attacks had ever been given to a charity called the Twin Towers Fund.

The White House did not respond to a question asking for clarification of Mr Trump’s involvement at ground zero.