The violence that flared in Porto was neither spontaneous nor unexpected. It followed months of vitriol on social media that came not only from disgruntled Portuguese, but also from prominent far-right figures inside and outside the country.

The posts linked a global network of agitators who have seized on the influx of migrants seeking political asylum or economic opportunity to build seething followings online.

Ideas like this once festered on the fringes of the internet but are now increasingly breaking through to the mainstream on social media platforms like X and Telegram, which have done little to moderate the content. The ability to clip and share videos and to instantly translate foreign languages has also helped make it easier to spread hateful material across geographic and cultural divides.

These networks peddle a toxic brew of bigotry online that officials and researchers say is increasingly stoking violence offline — from riots in Britain to bloody attacks in Germany and arson in Ireland. Establishing a direct correlation between online language and events in the real world is difficult, but researchers and officials said the evidence of a link has become overwhelming.

“What is said ultimately will shape what people will do,” said Rita Guerra, a researcher at the Center for Psychological Research and Social Intervention in Lisbon who studies online hate in Portugal. “That is why this is very concerning, not just for Portugal and Europe, but worldwide.”

‘Fuel for a Fire’

In Britain, false and inflammatory posts by white supremacists and anti-Muslim agitators set off clashes across the country after the stabbing deaths of three children in Southport, a town outside Liverpool, on July 29.

Posts on TikTok, YouTube, X and Telegram circulated false or unsubstantiated claims that the attacker was a Syrian refugee, when in fact he was from Wales.

Since then, unrest has convulsed Britain. Protesters clashed with the police, lit cars on fire and ransacked businesses.

“They used Southport as fuel for a fire,” Lee Marsh, a Liverpool resident, said at a demonstration against racism on Wednesday. “The only thing that should have happened online,” he added, “was support and respect for those families of the girls killed.”

The incendiary language inundated social media platforms despite their own policies prohibiting it, according to the Institute for Strategic Dialogue, a nonprofit research organization in London that has tracked the fallout of the stabbing. The companies, the organization said, lack “an understanding of the real-world impacts of misinformation” that appears on their platforms.

Elon Musk, the owner of X, himself weighed in on the events, declaring last weekend that “civil war is inevitable” in Britain.

Since Mr. Musk bought the platform, then known as Twitter, in 2022, the company has reinstated far-right figures who had previously been banned, leading to a sharp increase in hateful content on the platform. Mr. Musk has also used it to rail against governments he says have failed to bring immigration under control.

Representatives from Meta, X and TikTok did not respond to requests for comment. A spokesman for Telegram said “calls to violence are explicitly forbidden” by its terms of service.

YouTube, when contacted by The New York Times about this article, suspended the account of Grupo 1143, the extremist group organizing protests in Portugal. “Any content that promotes violence or encourages hatred of people based on attributes like ethnicity or immigration status is not allowed on our platform,” the company said, “and we’re committed to removing this content as quickly as possible.”

Immersed in Rabid Content

Racism and xenophobia have haunted the internet since the earliest dial-up connections, but they have, by most accounts, become pervasive in recent years.

Online influencers have weaponized the issue of immigration with disinformation and racist conspiracy theories, including one that predicts a “great replacement” of white people by nefarious global forces.

“Europe has been invaded by the world’s scum, without a single bullet being fired,” Tommy Robinson, one of Britain’s most notorious activists, wrote on X days before the attack in Porto in May. The post included a video with a voice over in Portuguese and subtitles in French.

Right-wing political parties in Europe have surged with the use of similar anti-immigrant language. In the United States, Donald J. Trump has made the influx of refugees and migrants a central issue in this year’s presidential election.

Russia, too, has used immigration as a cudgel in its propaganda in Europe, amplifying incidents and protests, including the recent unrest in Britain, through its state media and covert bot networks.

European governments have stepped up warnings about the threat of extremism online, but they are struggling to find effective ways to respond while respecting freedoms of speech and assembly.

In the Netherlands, the National Coordinator for Counterterrorism and Security warned last year that people “can immerse themselves in rabid content for years, until an isolated incident incites them to concrete violence.”

After the recent violence in Britain, the government urged the public to “think before you post,” warning that hateful messages could amount to a crime. On Friday, a man from Leeds was sentenced to 20 months for posts on Facebook calling for attacks on a hotel housing asylum seekers. Among hundreds of people arrested was a 55-year-old woman from near Chester for a social media post said to “stir up racial hatred.”

“The internet has evolved from a passive cheering section to the active shaping and fomenting of ethnic and sectarian conflict,” said Joel Finkelstein, a founder of the Network Contagion Research Institute in New Jersey, which studies threats online. “This new reality poses a profound challenge to democracies, which find themselves ill-equipped to manage the rapid dissemination of these dangerous ideas.”

A Front Line

In 2023, researchers from the Network Contagion Research Institute and two universities documented a hashtag was going viral across Ireland that said the country was full. It was used to promote demonstrations in cities across the country against efforts to build housing for migrants.

One of the researchers, Tony Craig of Staffordshire University in England, warned that the campaign would inevitably lead to violence. “It’s going to get worse,” he said last summer.

He was prescient.

In November, a homeless immigrant from Algeria stabbed three children and their guardian in Dublin. Within hours, the internet churned with calls for protest — and retaliation — and soon hundreds rioted on Parnell Square in the city’s center. It was the worst public unrest in Ireland in years.

After the riots, the government vowed to toughen the law against incitement. “It’s not up-to-date for the social media age,” Leo Varadkar, the prime minister then, said.

The challenge is that the incitement also comes from outside their borders. Only 14 percent of posts on X about the stabbings and resulting outcry originated in Ireland, according to an analysis by Next Dim, a company that tracks activity online.

Since then, accounts online have continued to foment anger. This year, agitators circulated maps with the locations of migrant housing, which have become targets. Outside one center in June, protesters slit the throats of three pigs as a threat to Muslims believed to be living there.

Last month, a former paint factory being converted to housing for asylum seekers in Coolock, near Dublin, became a new flashpoint.

As anger about the project spread online, arsonists twice attacked the building. On July 19, hundreds gathered nearby, leading to a violent confrontation with the police.

Driving the Conversation From Afar

A leading figure in the growing chorus of bigotry online has been Mr. Robinson, the notorious activist whose real name is Stephen Yaxley-Lennon.

Mr. Robinson has been known for his ardent anti-immigration views for more than a decade, but by 2019 he faced bans or other restrictions on Facebook, Instagram, X and YouTube for spreading hateful content and struggled to find much of an audience online.

Then, last November, X reinstated Mr. Robinson. (“I’m back!” his profile declares). He now has more than 960,000 followers on the platform.

Mr. Robinson’s prolific posts are widely shared across like-minded accounts on other platforms and in other countries.

An example of his reach was clear in March, when he reacted to news of a fire at a migrant housing center in Berlin. He posted a brief video clip on Telegram claiming that migrants had deliberately set fire to the center, located in the city’s old Tegel Airport, “in hope of securing better” accommodations.

His followers replied with a torrent of hateful and racist comments, according to an analysis by the SITE Intelligence Group. Though the cause of the fire remained unclear, the insinuation that it was intentional caromed from Britain to the Netherlands and Portugal and back to Germany.

Joe Düker, a researcher at the Center for Monitoring, Analysis and Strategy, an organization in Germany that studies extremism, said Mr. Robinson’s post helped drive the narrative in Germany, where the authorities reported 31 violent crimes against migrants in the first three months of this year. An extremist group active in Austria and Germany, Generation Identity Europa, forwarded his post on Telegram to its own followers.

Asked whether he believes his social media posts contribute to violence, Mr. Robinson responded: “I believe the teachings in the Koran contribute to violence. Shall we ban it?”

Other figures have similar international reach, including Eva Vlaardingerbroek in the Netherlands, Martin Sellner in Austria and Francesca Totolo in Italy. They often amplify one another’s posts, forming a global echo chamber of hatred toward migrants.

“There isn’t enough of an appreciation of how transnational these networks are,” said Wendy Via, a founder of the Global Project Against Hate and Extremism, an organization in the United States that tracks the spread of racism.

‘Whoever riots gets heard’

In the initial hours after the stabbing attack in England, when little information was released by the authorities, agitators quickly stepped into the void.

By the time officials said that the suspect was a 17-year-old British citizen from Wales, it was too late. Angry calls for protests had swept TikTok, Telegram and X, calling people into the streets. “Whoever riots gets heard,” Mr. Robinson declared. “The British need hearing.”

One Telegram channel created to discuss the stabbing shared the address of 30 locations to target for protest. The platform blocked the channel, but only after it had swelled to more than 13,000 members.

“They won’t stop coming,” one member of the group said, “until you tell them.”