Billionaire Elon Musk sparked controversy Monday after making a gesture at an event celebrating US President Donald Trump's inauguration, with some calling it a "Nazi" or "fascist" movement.

The X, SpaceX and Tesla chief appeared on stage at the Capital One Arena in Washington, where supporters of the newly inaugurated president had gathered for a rally.

Upon thanking the crowd for returning the 78-year-old Republican to the White House, Musk tapped the left side of his chest with his right hand and then extended his arm with his palm open, repeating the gesture for the crowd seated behind him.

Claire Aubin, a historian who specializes in Nazism within the United States, agreed Musk's gesture was a "sieg heil," or Nazi salute.

"My professional opinion is that you're all right, you should believe your eyes," Aubin posted on X, aligning with those who found the gesture was an overt reference to Nazis.

Ruth Ben-Ghiat, a historian of fascism, also found the gesture "was a Nazi salute -- and a very belligerent one too," she said on X.

Democratic Party members also quickly responded with alarm.

Congressman Jimmy Gomez reacted to the moment by posting on X: "Well, that didn't take long."

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Musk, who has posted a dozen times on his social network X since making the gesture, did not immediately react to the swirling controversy.

One attendee at the rally told AFP he thought Musk was making the gesture as a joke.

"He's very humorous, and he uses a lot of sarcasm. So when he did that on the stage, I don't think he meant it," said Brandon Galambos, a 29-year-old pastor and tech worker.

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Reports by Wired and Rolling Stone magazines said far-right personalities in the United States were celebrating the move, like the writer Evan Kilgore, who called the salute "incredible."

Musk has also made several statements in recent weeks in support of Germany's far-right AfD party and British anti-immigration party Reform UK.

The Anti Defamation League (ADL), an organization founded to combat anti-Semitism which has criticized Musk in the past, defended his actions this time around.

"It seems that Elon Musk made an awkward gesture in a moment of enthusiasm, not a Nazi salute," the organization said in a statement posted on X.

Democratic Representative Alexandria Ocasio-Cortez blasted the ADL's reaction, saying on X: "Just to be clear, you are defending a Heil Hitler salute that was performed and repeated for emphasis and clarity."

Another historian, Aaron Astor, also rebuffed accusations of Musk's Nazi emulation.

"I have criticized Elon Musk many times for letting neo-Nazis pollute this platform," he wrote on X, adding: "But this gesture is not a Nazi salute."

"This is a socially awkward autistic man's wave to the crowd where he says 'my heart goes out to you.'"

In 2021, Musk announced he had been diagnosed with Asperger's syndrome, a form of autism.

© Agence France-Presse