Behind a black door just steps from the golden domes of Novodevichy monastery, a group of young men and women sit huddled at computers. They are surrounded by racks of the red and white jumpers and scarves that mark the devoted fans of FC Spartak, Moscow's leading football club.

This is the headquarters of Fratria, the unofficial Spartak fan club that lost one of its members when he was killed during a brawl with a gang from the Caucasus, the restive mainly Muslim region on Russia's southernmost flank.

The shooting of Yegor Sviridov on 6 December has sparked the worst race riots Moscow has seen since the fall of the Soviet Union. The killing and beating of immigrants has increased, racist and anti-Semitic graffiti has proliferated, and the atmosphere is tense.

For the past week, groups of roaming youth have taken to the streets daily, shouting "Russia for Russians! Moscow for Muscovites!" The youths manning the shop at Fratria insist they are not involved. "We only support legal, peaceful forms of protest," says Lena Sekhina, the club's press secretary.

Russia has a growing racism problem, with nationalist feelings increasingly stoked by the government since the collapse of the Soviet Union left an ideological vacuum. Yet many are beginning to wonder why tensions have finally boiled over. There are the conspiracy theories that say the unrest was stoked by the government of Vladimir Putin to prove the need for his authoritarian rule.

Others wonder whether nationalist groups are taking advantage of the weakened political climate following the dramatic firing of Moscow's veteran mayor, Yury Luzhkov, two months ago.

For Yevgeny Valyaev the cause is clear. "It's not one death. It's a pressure that's been building for several years," said the shaven-headed leader of Russky Obraz, an ultra-nationalist group that helped gather some of the 5,000 men who descended upon the Kremlin on 11 December, launching the current unrest. "There was no way we could not gather – because he was a football fan and because he was Russian," he said, referring to Sviridov. "It was a protest against ethnic banditry."

The link between ultra-nationalism and football has flourished in Russia, which boasts some of the rowdiest supporters in Europe. On Friday, UEFA fined Spartak €75,000 (£63,600) after its supporters invaded the pitch during a Champions League match away to Zilina in Slovakia. Several Russian clubs have been fined over the years after supporters waved racist banners referring to African players as monkeys.

It is a problem that has been years in the making. Russia has eight years to prepare for its role as host of the 2018 World Cup. Some are concerned that while eight years may be enough time to build stadiums and travel infrastructure, it may not be enough to transform a national mind-set.

"I have always been a patriot," said Valyaev, a stocky 23-year-old who also helps organise the annual neo-Nazi rally in Moscow. "We think the interests of the race should be above the interests of the government – the government must work for the race. To stop this wave now, people must see that their protests have been heard."

Four days after the Kremlin riot, youths gathered in sites around Moscow, shouting racist slogans and standing off with the hundreds of riot police called in to control them. More than 1,000 people were arrested.

Skinheads were few, outnumbered by adolescent boys and girls who had latched on to the nationalist wave. On Thursday, police arrested three teenagers, including a 14-year-old boy, on suspicion of involvement in the stabbing to death of a Kyrgyz man last weekend.

The unrest has already spread to other cities – St Petersburg, Rostov-on-Don, Samara. All are due to host stadiums for the 2018 World Cup. "For a long time, this hasn't just been a problem for just Spartak fans and football fans," said Ivan Kuznetsov, a spokesman for the All-Russian Union of Fans, referring to the influx of migrants to the Russian capital. "This is a problem for all the youth of Moscow and other cities."

He was referring mainly to men from the Caucasus – Chechnya, Dagestan and the other dozen republics that, while a part of the Russian Federation, have never been culturally integrated.

"Kids who are at school, university, who have girlfriends – they're constantly running up against aggressive Caucasian youth," he said.

The problem is further complicated by the fact that much of Moscow's police force fought in Chechnya to put down the republic's separatist rebellion. The conflict, marked by widespread human rights abuses, left lasting scars. In dealing with the riots, police have avoided harsh tactics and some have even appeared sympathetic.

The football fans and skinheads do not fear them. Still, Valyaev has, for the past three years, carried an air pistol whenever he leaves the house. "I've never had to use it, but I want to make sure if a situation arises where it needs to be used, it is close."