Apart from allegedly wanting to kill radical leftists and bomb a TV network widely reported to be CNN, 24-year-old US Army private Jarrett William Smith, charged on Sept 23, also wanted to travel to Ukraine to join the Azov Battalion.

It is a far-right paramilitary group, apparently integrated into Ukraine's National Guard. Its former leader Andriy Yevhenovych Biletsky is now an MP, leading the National Corps party.

The charges against Smith indicate that his apparent mentor, a man called Craig Lang, had fought with a right-wing paramilitary group in Ukraine similar to the Azov Battalion.

Ukraine has attracted around 17,000 foreign fighters from over 50 countries, the vast majority from Russia. Of the 2,000-odd non-Russian foreign fighters, around 35 are Americans, says a new report from the Soufan Centre, a security think-tank.

As Iraq and war-torn Syria were petri dishes for the Islamic State in Iraq and Syria (ISIS), Ukraine has become a "playground" for another kind of extremist, it warns.

"White supremacists now have their own theatre in which to learn combat - Ukraine, where the conflict between pro-Russian separatists and Ukrainian government forces has been raging since 2014, attracting fighters from around the globe who are fighting on both sides," says the report.

"White supremacists are forming global networks, much as jihadis did prior to 9/11, and are learning from jihadi tactics," it warns.

"In terms of organisational structure, white supremacists adopted the leaderless resistance model of terrorism before jihadis ever did, relying on attacks by lone actors as a means of minimising infiltration of the movement by federal law enforcement agents in the 1980s."

At a Sept 17 House Homeland Security Committee hearing, Soufan Centre CEO Ali Soufan, a former FBI supervisory special agent who had worked on several high-profile international cases, said: "Supremacists make propaganda warning of an alleged great replacement of whites in the same way jihadis talk about supposed war against Islam.

"White supremacists support violence... to defend the purity of the race just as jihadis use violence to protect the purity of the religion. Both groups recruit followers and reinforce their messages through social media. While jihadis make online videos, supremacists post online manifestos.

"Where jihadis travel to fight in places like Syria and Afghanistan, white supremacists now have their own theatre in which they learn combat: Eastern Ukraine."

The report's warning is aimed mostly at the United States.

Another organisation that tracks hate, the Anti-Defamation League, has reported that, over the past decade, white supremacy extremists have been responsible for three times as many deaths in the US as have Islamists.

In May, a senior FBI official told Congress that the bureau was pursuing about 850 domestic terrorism investigations, of which a "significant majority" were related to white supremacist extremists.

The report says: "By nearly every metric, white supremacy extremism has become one of the single most dangerous terrorist threats facing the United States, if not the single most dangerous." It urges an update of US legal statutes to robustly deal with the threat.

Contemporary white supremacist groups may yet be small and inchoate - unlike ISIS, which carved out territory for itself. But some ideological foundations are common to most, if not all.

Writer Renaud Camus, said to live in a chateau in France, propounds a theory of "great replacement" of France's original white European population by new arrivals, mostly from Africa, which has become a far right talking point cited by mass killers as far away as Christchurch, New Zealand, and El Paso, Texas.

Political extremism expert Rudy Reichstadt, from the Fondation Jean-Jaures research institute, told the New York Times: "It's a slogan that dramatises the situation, talking of great replacement the same way we speak of the great barbarian invasions."

The ground in Ukraine is fertile for white males with a sense of grievance and disenfranchisement, who believe multiculturalism is degrading white values, Mr Jason Blazakis, one of the lead authors of the report and a senior fellow at the Soufan Centre, told The Straits Times.

Mr Blazakis, who is also professor of practice at the Middlebury Institute of International Studies in Monterey, California, said: "Russia's (2014) incursion into Crimea using separatists, and proxies on both sides, created a zone in which white supremacists can develop tactics, techniques and procedures and general trade craft."