BERLIN — When insurrectionists stormed the Capitol in Washington this month, far-right extremists across the Atlantic cheered. Jürgen Elsässer, the editor of Germany’s most prominent far-right magazine, was watching live from his couch.

“We were following it like a soccer match,” he said.

Four months earlier, Mr. Elsässer had attended a march in Berlin, where a breakaway mob of far-right protesters tried — and failed — to force their way into the building that houses Germany’s Parliament. The parallel was not lost on him.

“The fact that they actually made it inside raised hopes that there is a plan,” he said. “It was clear that this was something bigger.”

And it is. Adherents of racist far-right movements around the world share more than a common cause. German extremists have traveled to the United States for sniper competitions. American neo-Nazis have visited counterparts in Europe. Militants from different countries bond in training camps from Russia and Ukraine to South Africa.

For years far-right extremists traded ideology and inspiration on societies’ fringes and in the deepest realms of the internet. Now, the events of Jan. 6 at the U.S. Capitol have laid bare their violent potential.

In chatter on their online networks, many disavowed the storming of the Capitol as amateurish bungling. Some echoed falsehoods emanating from QAnon-affiliated channels in the United States claiming that the riot had been staged by the left to justify a clampdown on supporters of President Donald J. Trump. But many others saw it as a teaching moment — about how to move forward and pursue their goal of overturning democratic governments in more concerted and concrete ways.

It is a threat that intelligence officials, especially in Germany, take seriously. So much so that immediately after the violence in the United States, the German authorities tightened security around the Parliament building in Berlin, where far-right protesters — waving many of the same flags and symbols as the rioters in Washington — had tried to force their way in on Aug. 29.

President Biden has also ordered a comprehensive assessment of the threat from domestic violent extremism in the United States.

For now, no concrete plans for attacks have been detected in Germany, officials said. But some worry that the fallout from the events of Jan. 6 have the potential to further radicalize far-right extremists in Europe.

“Far-right extremists, corona skeptics and neo-Nazis are feeling restless,” said Stephan Kramer, the head of domestic intelligence for the eastern German state of Thuringia. There is a dangerous mix of elation that the rioters made it as far as they did and frustration that it didn’t lead to a civil war or coup, he said.

Meeting online and in person

It is difficult to say exactly how deep and durable the links are between the American far right and its European counterparts. But officials are increasingly concerned about a web of diffuse international links and worry that the networks, already emboldened in the Trump era, have become more determined since Jan. 6.

A recent report commissioned by the German foreign ministry describes “a new leaderless transnational apocalyptically minded, violent far-right extremist movement” that has emerged over the past decade.

Extremists are animated by the same conspiracy theories and narratives of “white genocide” and “the great replacement” of European populations by immigrants, the report concluded. They roam the same online spaces and also meet in person at far-right music festivals, mixed martial arts events and far-right rallies.

“The neo-Nazi scenes are well-connected,” said Mr. Kramer, the German intelligence official. “We’re not just talking about likes on Facebook. We’re talking about neo-Nazis traveling, meeting each other, celebrating together.”

The training camps have caused anxiety among intelligence and law enforcement officials, who worry that such activity could lay the groundwork for more organized and deliberate violence.

Two white nationalists, who attended a paramilitary camp run by the extremist Russian Imperial Movement outside of St. Petersburg, were later accused by Swedish prosecutors of plotting bombings aimed at asylum seekers. Last year, the United States State Department designated the Russian Imperial Movement a terrorist organization, the first white nationalist group to receive the label.

In 2019, the F.B.I director, Christopher Wray warned that American white supremacists were traveling overseas for training with foreign nationalist groups. A report that year by the Soufan Center, a nonpartisan think tank, found that as many as 17,000 foreigners, many of them white nationalists, had traveled to Ukraine to fight on both sides of the separatist conflict there. Among them were several dozen Americans.

Sometimes they inspire one another to kill.

The hate-filled manifestos of Anders Breivik, who killed 77 people in Norway in 2011, and Dylann Roof, an American white supremacist who killed nine Black parishioners in South Carolina four years later, influenced Brenton Harrison Tarrant, who in 2019 live-streamed his murder of over 50 Muslims in Christchurch, New Zealand.

Mr. Tarrant’s manifesto, titled “The Great Replacement,” in turn inspired Patrick Crusius, who killed 22 people in El Paso, Texas, as well as a Norwegian gunman who was overpowered as he tried to shoot people at a mosque in Oslo.

Many far-right extremists immediately interpreted Jan. 6 as both a symbolic victory and a strategic defeat that they need to learn from.

Mr. Elsässer, the editor of Compact magazine, which Germany’s domestic intelligence agency classifies as extremist, described the storming of the Capitol as “an honorable attempt” that failed because of inadequate planning.

“The storming of a parliament by protesters as the initiation of a revolution can work,” he wrote the day after the riot. “But a revolution can only be successful if it is organized.”

“When it’s crunchtime, when you want to overthrow the regime, you need a plan and a sort of general staff,” Mr. Elsässer wrote.

Among those feeling encouraged by the mobilization seen on Jan. 6 was Martin Sellner, the Austrian head of Europe’s far-right Generation Identity movement, who preaches nonviolence but has popularized ideas like “the great replacement.”

After the storming of the Capitol, Mr. Sellner wrote: “The anger, pressure and the revolutionary mood in the camp of the patriots is in principle a positive potential.”

“Even though it fizzled out pointlessly in the storm on the Capitol, leaving behind no more than a few memes and viral videos,” he wrote, “one could form an organized and planned approach out of this mood for a more effective resistance.”

Mr. Sellner, who said in an interview that Mr. Trump would be even more galvanizing in opposition, personifies the reach of an increasingly global movement with his close links to activists across Europe and the United States. He is married to Brittany Pettibone, an American alt-right YouTube star who has interviewed prominent European extremists like the British nationalist Tommy Robinson.

Mr. Robinson met virtually with the American leader of the far-right Proud Boys, Enrique Tarrio, for an hour-and-a-half-long conversation on Nov. 19 that was billed as a unity summit to discuss the outcome of the American election.

The men spoke of their common struggle, against liberals, antifa (a loosely affiliated group of far-left anti-fascism activists) and the big tech companies that had barred both men from their platforms. They also spoke of the U.S. presidential election outcome in existential terms, warning that if the right failed to preserve the presidency for Mr. Trump, it risked annihilation.

The Democrats, Mr. Robinson said at one point, are going to “replace you like we’ve been replaced.”

“The borders will open, and they’ll replace you with foreign people,” he said.

Gaining traction in Germany

Several members of the Proud Boys, whom Mr. Trump famously told to “stand back and stand by,” were among those who stormed the Capitol.

On Oct. 19, the Proud Boys shared on one of their Telegram groups that they had seen “a huge uptick in support from Germany over the last few months.”

“A high percentage of our videos are being shared across Germany,” read a message in the Telegram group that was also translated into German. “We appreciate the support and we are praying for your country. We stand with the German nationalists who do not want migrants destroying their country.”

Over the past three months, the Proud Boys posted several videos of German police officers confronting left-wing protesters in Berlin. In two of the videos, which feature the police violently beating a protester, the Proud Boys cheered the violence.

Although they mocked Mr. Trump as “a total failure” after he disavowed the Capitol rampage and left the White House, they have voiced support for far-right groups in other countries including France, Poland and Turkey.

And as America has exported QAnon conspiracy theories across the Atlantic, European conspiracy theories and disinformation are also making their way to the United States.

Within days of the U.S. election, German QAnon followers were spreading disinformation that they said proved that the vote had been manipulated from a C.I.A.-operated server farm in Frankfurt, though millions of votes were cast by paper mail-in ballots.

The disinformation, which the German researcher Josef Holnburger traced back to a German-language account, was amplified by at least one local chapter of Alternative for Germany, the far-right political party known by its German initials, AfD. It also ended up being highlighted by U.S. Representative Louie Gohmert and Rudy Giuliani, the Trump ally and former mayor of New York City.

From there, it went viral — a first for a German QAnon conspiracy in the United States, Mr. Holnburger said.

The transnational links are inspirational rather than organizational, said Miro Dittrich, an expert on far-right extremist networks. “It’s not so much forging a concrete plan as creating a violent potential,” he said.

Yet experts remain skeptical of the potential to forge more durable trans-Atlantic relations among far-right groups. Almost all such attempts since World War II have failed, said Anton Shekhovtsov, an expert on the European far right at the University of Vienna.

Most recently, Stephen K. Bannon, the architect of Mr. Trump’s successful 2016 presidential bid, toured Europe several years ago trying to knit together populist nationalist parties like Marine Le Pen’s National Rally in France and Alternative for Germany.

“It was a fiasco, Mr. Shekhovtsov said. “Bannon was pushing very old white supremacist ideas. This is no longer accepted in Europe. You may be a radical-right-wing populist, but you can’t talk about white nationalism.”

Differing expectations

There’s even division among far-right followers about whether such alliances are valuable or viable. For many, the idea of an international nationalist movement is an oxymoron.

“There is a common mood and an exchange of ideas, memes and logos,” said Mr. Sellner, the Austrian far-right campaigner. “But the political camps in Europe and America are very different.”

Rinaldo Nazzaro, the founder of the international white-nationalist group The Base, now lives in self-imposed exile in St. Petersburg, Russia, but says he has no interest in forging ties with Russian nationalist groups.

“Nationalists in America must do the heavy lifting themselves,” he said. “Outside support could only be supplemental, at best.”

Others, like Matthew Heimbach, an organizer of the 2017 violent far-right protest in Charlottesville, Va., disagree.

“American members of the far right and white nationalist groups have been trying to get Europe to return their calls for a decade now,” he said in an interview.

With some success, he spent years working to forge alliances with like-minded groups in the Czech Republic, Germany and Greece.

He even hosted a delegation from the Russian Imperial Movement in 2017, several years before the United States declared it a terrorist organization. Members of the group, which runs paramilitary-style camps to train Russian and foreign nationalists in military tactics, spent two weeks in the United States and traveled extensively.

Photographs of the trip show Mr. Heimbach and one of the group’s leaders, Stanislav Shevchuk, posing with a Russian imperial flag in front of the White House and the U.S. Capitol.

Mr. Heimbach, who denounced the Jan. 6 Capitol riot and claims to have renounced white nationalism, said he had also taken his Russian guests to Dollywood and the Country Music Hall of Fame in Tennessee.

The trip, Mr. Shevchuk later wrote, “opened my eyes to a different alt-right America and I was convinced that we Russians had a lot in common with them.”

Katrin Bennhold reported from Berlin, and Michael Schwirtz from New York. Sheera Frenkel contributed reporting from San Francisco, and Christopher F. Schuetze from Berlin.