At least five people were arrested after fireworks, flares and glasses were thrown between supporters in Bilbao.
French authorities had for months been seeking the suspect, who was not named and, along with several other Russian hooligans, is accused of attacking 51-year-old England fan Andrew Bache ahead of the Russia-England match in Marseille.
The Spanish league said it "deplores and condemns the death" of the police officer, and its president said he hoped the world and European soccer governing bodies would take action to halt fan violence. "We do not know if they are all supporters of Spartak, but many of them are Russians", the spokesman for Ertzaintza added.
The incident late on February 22 raised concerns less than four months before Russian Federation is set to host the World Cup.
González told Sputnik that he went to Athletic's match in Moscow and that not only did he suffer no aggressive attitude from Russian fans, he "felt welcome".
Videos of fireworks and flares being let off were widely shared on social media ahead of the fixture at San Mames, as pre-match calls for calm were ignored.
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Police said Friday five people remained detained - three Russian nationals and two Spaniards.
Russian local authorities are putting strict security procedures in place to counter hooliganism during the world cup tournament scheduled for June.
"Everything was very confusing and the police did not distinguish Athletic Bilbao's fans from the Spartak because they all wear the same colors".
Federation Internationale de Football Association said it "deeply regrets" the incident but did not assign any blame. "Authorities should make lists of radical fans to make sure these people can't get visas and travel overseas to see away games".
A Spanish police officer dies after violent clashes between Athletic Bilbao and Spartak Moscow supporters on Thursday night. "And that's what happened - when you are attacked, you fight back", Izmailov explained.
After the game, Athletic Club tweeted their condolences. "They proceed in an atmosphere of hospitality, safety and comfort for the fans".
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