The match in Wroclaw was marred by allegations of racism and violence.
It is understood UEFA are considering whether to take action against the Russian Football Federation after anti-racism campaigners claimed Czech defender Theodor Gebre Selassie was the victim of monkey chants during Friday night's Group A game.
And European football's governing body were also deciding if they would sanction Russia after their fans were caught on camera attacking stewards in a walkway at the Municipal Stadium.
Euro 2012 is only two days old but it is already in danger of being spoilt by fan behaviour, with two incidents of alleged monkey chants at stadia inside 48 hours, and numerous reports of violence across Poland and Ukraine.
The FARE (Football Against Racism in Europe) network has confirmed one of their observers at Friday night's Russia-Czech Republic game heard "fleeting" racist abuse of Gebre Selassie.
Asked if it included monkey chants, FARE chief executive Piara Powar said: "Our observer reported descriptions of that nature.
"It was directed at the Czech Republic's only black player."
Powar said the abuse came from a "small section of the crowd" and admitted: "It may not be easy to pull together evidence for a case to be brought."
UEFA asked FARE to help appoint expert spotters to report offensive banners, chants and behaviour in stadiums.
Powar also confirmed "Russian Empire" flags were displayed during Friday night's game, which Russia won 4-1.
The Czech Republic camp were not immediately available for comment but it is understood they had not made a formal complaint over the alleged abuse of Gebre Selassie on Saturday afternoon.
Friday was the second time in two days black players were said to have been subjected to monkey chants in Poland after members of the Holland squad were racially abused during a training session in Krakow.
Violence also erupted at the Russia-Czech Republic game when a handful of stewards were attacked by large group of fans inside the 40,000-capacity ground.
Footage of the incident has emerged online and UEFA said in a statement: "UEFA is aware that at yesterday's Group A match in Wroclaw between Russia and the Czech Republic there was a brief and isolated incident involving a small group of around 30 fans who attacked a handful of stewards.
"The situation was quickly and efficiently brought under control. The local police are aware of the incident and investigating.
"The cause of the incident is not currently known but we are studying the security reports and available images.
"UEFA remains entirely committed to the safety and security of all fans and spectators at all matches of Euro 2012."
Police spokesman Mariusz Sokolowski was reported by Eurosport to have said: "I can confirm that this happened at the stadium.
"The attackers were from the group of Russian language fans. We are trying to identify them.
"Police have the security footage from the stadium. We are looking into it."
Reports claimed four members of stadium staff were taken to hospital and released later that evening.
The footage shows one steward left in a heap on the ground after being set upon by several assailants before the violence dissipated and he is helped to his feet, while another is kicked in the head while trying to evade a lone attacker.
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