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"I just want to say thank you for making it happen," Musk said during a speech at Capital One Arena, referring to Donald Trump's victory in the presidential election. He slapped his hand on his chest, then extended his arm straight out and up with his palm down.

"My heart goes out to you," Musk said after turning around to make a similar gesture facing the other way.

Many social media users noticed the gesture looked like a Nazi salute. Musk fanned the flames of suspicion by not explicitly denying those claims in a dozen posts since, though he made light of the criticism and lashed out at people making that interpretation.

"The 'everyone is Hitler' attack is sooo tired," Musk posted on X hours after he left the stage.

Critics and fans alike of the Tesla CEO and world's richest man were quick to react to the gesture.

"The White Flame will rise again," a chapter of the white nationalist group White Lives Matter posted on Telegram.

"Maybe woke really is dead," white nationalist Keith Woods posted on X.

"Did Elon Musk just Heil Hitler …" right-wing commentator Evan Kilgore posted on X. "We are so back."

The Anti-Defamation League, an antisemitism and human rights watchdog, called it an "awkward gesture" and urged caution in jumping to conclusions. Other extremism monitors and experts pointed out it was unclear what Musk was trying to convey to the crowd of Trump's supporters by thrusting out his arm.

"I'm skeptical it was on purpose," said Jared Holt, a senior research analyst at the Institute for Strategic Dialogue, which tracks online hate. "It would be an act of self-sabotage that wouldn't really make much sense at all."

Holt noted Musk specifically said his heart went out to the crowd, which could indicate a sort of gesture of thanks.

Since Musk bought Twitter, now called X, the self-described "free speech absolutist" faced criticism from hate-speech watchdogs for allowing extremist, dangerous and antisemitic comments to flourish on the social media platform.

His response was to attack his critics, suing one group unsuccessfully after advertisers fled X and threatening to sue another, the Anti-Defamation League, which urged calm at what it called a "delicate moment" in its statement Monday.

"It seems that @elonmusk made an awkward gesture in a moment of enthusiasm, not a Nazi salute, but again, we appreciate that people are on edge," the ADL said in a statement. "In this moment, all sides should give one another a bit of grace, perhaps even the benefit of the doubt, and take a breath."

Kurt Braddock, a professor of communication at American University who studies extremism, radicalization and terrorism, said the gesture was a fascist salute and "people shouldn't doubt what they saw."

"I know what I saw, I know what the response to it was among elements of the extreme right including neo-Nazis, Braddock said. "And none of it is a laughing matter."

Efraim Zuroff, the retired head of the Simon Wiesenthal Center's Jerusalem office and formerly the organization's top Nazi hunter, said he also saw it as Nazi salute, and that it happened at U.S. presidential inauguration celebration made it especially shocking to see.

"It's totally improper, and it raises all sorts of questions regarding his motivations, or his ignorance," he said in a telephone interview from Israel. "This is America, the leader of the free world, the people who sacrificed 200,000 soldiers who died to defend Europe. He has to explain himself."

In Europe where the fascist salute is associated with the hate, death and destruction of World War II, Musk's arm gesture elicited outrage.

An Italian communist youth organization hung an effigy of Musk upside down Tuesday in Milan's Piazzale Loreto, where dictator Benito Mussolini's body was hung upside down after he was executed during the final days of WWII. The organization, Cambiare Rotta (Change Course), noted in a Facebook post that the social media company removed a photo of the effigy.

"We are correctly a little afraid, because that image is scary," author Filippo Ceccarelli told Italian La7 private television.

Known as the Roman salute in Italy, the straight-arm greeting officially adopted in 1925 by Mussolini's fascist regime is banned in Italy though it is rarely prosecuted.

Musk's representative in Italy, Andrea Stroppa, published the photo on X with the words: "Roman Empire is back, starting with the Roman salute," according to the news agency ANSA.

He later deleted the post, writing that Musk was expressing his emotions but denying he emulated fascism.

"He does not like extremists," Stroppa wrote.

In France on Monday, more than 80 associations, including human rights, environmental and press freedom groups left X, though it is unclear if Musk was the trigger or Trump's inauguration. Several universities and schools left X, too, as well as nationwide and local newspaper on various sides of the political spectrum.

Brian Levin, founder of the Center for the Study of Hate and Extremism at California State University, San Bernardino, said even if it was accidental, Musk's gesture has the power to hurt people.

"When you're a public figure at the highest echelons of power on Inauguration Day, doing a salute like that is extraordinarily disturbing and it calls for an explanation from Musk," he said. "Points are made about free speech. Well, along with free speech comes responsibility."

Levin said some extremists will take the gesture regardless of its intent as "some kind of not-so-subtle marching order."