European football's governing body slapped a 120,000-euro ($150,000, 96,000-pound) fine on the Football Union of Russia (RFS) after supporters set off and threw fireworks during the Group A opener with the Czech Republic in Wroclaw, Poland.
Police are also hunting Russian fans who attacked four volunteer stadium stewards after the match, following the broadcast of amateur video footage of a brawl inside the ground.
UEFA initiated disciplinary proceedings over the incidents last week, as well as over the display of potentially inflammatory "Russian Empire" flags at the ground in the southwest of the country.
The flags can be seen as deeply provocative in parts of Eastern Europe that used to be under Moscow's thumb, including Poland, and were reported by a UEFA-backed racism monitoring body.
"The UEFA Control and Disciplinary Body has today (Wednesday) decided to impose a deduction of six points on the Football Union of Russia (RFS) in the qualifying round of the next UEFA European Football Championship," UEFA said in an emailed statement.
"This decision is suspended for a probationary period running from now until the end of the play-offs of the next UEFA European Football Championship (UEFA Euro 2016).
"The Football Union of Russia (RFS) has also been fined 120,000 euros ."
The behaviour of Russia's fans has been under scrutiny since their 4-1 win over the Czech Republic, with UEFA also investigating claims that a section of supporters racially abused Theodor Gebre Selassie, who is of Ethiopian origin.
Never Again, a Polish-based organisation part of the Football Against Racism in Europe (FARE) network, said Selassie, who is black, heard monkey chants during the game.
Racism was seen as a concern even before the start of Euro 2012 in Poland and Ukraine, which is the first-ever edition of the quadrennial competition to be held behind the former Iron Curtain.
UEFA and the co-hosts have had to deny reports that far-right extremists are rife at football grounds in both countries, while Dutch players said they were abused during a public training session in the southern Polish city of Krakow.
There was no immediate response from the Russian football federation but the national side was at the centre of a highly charged match against old foes Poland in Warsaw on Tuesday, which took place against the backdrop of massive security.
More than 180 supporters were detained after police were forced to use water cannon, tear gas and rubber bullets to disperse violent fans who clashed on the streets of Warsaw.
Police, who had 6,000 officers out in force, arrested 157 Poles and 24 Russians, as well as a Spaniard, a Hungarian and an Algerian. Ten police officers were treated for injuries, as well as 10 fans.
The match itself ended 1-1.
UEFA said it condemned the violence, calling those involved "groups of known troublemakers" rather than genuine fans, while Polish Prime Minister Donald Tusk said those involved were "idiots" who would feel the full force of the law.
Russian fans set off and threw at least two firecrackers on to the pitch after Dzaegov's goal but there were no other apparent incidents inside the showpiece sports venue, AFP reporters and photographers at the match said.
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