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The statement continued:
"Those who use sporting arenas to declare theirown personal political, or any other, position have no place in the stands.
"In this regard the RFU and the Russian national team strongly request all true fans to reject the provocative actions of hooligans and offer full co-operation to the organisers of matches in respect of the provision of security.
"We are addressing all fans who are in Poland. Remember that you represent your country. Respect yourself, your homeland and your team."
The Russian Football Union has released a statement following the news that UEFA have opened disciplinary proceedings against Russia over the behaviour of their fans during their European 2012 victory over Czech Republic on Friday.
"The Russian national team has begun its Euro 2012 campaign. At this team our team needs the support of its fans as never before. During the first game of the tournament against the Czech Republic, leading 4-1, our fans showed brilliant support for the team.
"The national team's players particularly noted that the unwavering support of fans inspired them to victory.
"At the same time we believe that some people who came to the stadium committed actions which were ill-fitting of true football fans."
Asian England football fans in Ukraine have spoken about the pressure put on them by family and friends not to travel to Euro 2012 over fears of racism.
Rikesh Solanki and his friend Amal Samji ignored the warnings and went ahead with their plans to watch England against France in Donetsk.
The Arsenal fans, who both work as brokers in the City of London, said they had found Ukraine and the people they had met very positive and welcoming.
UEFA have opened disciplinary proceedings against Russia over the behaviour of their fans during their European Championship victory over Czech Republic.
Anti-racism campaigners claimed Czech defender Theodor Gebre Selassie was the victim of monkey chants during last night's Group A game in Wroclaw, while fans were caught on camera attacking stewards in a walkway at the Municipal Stadium.
UEFA tonight decided to take action:
"UEFA has today announced that disciplinary proceedings have been opened against the Football Union of Russia (RFS) for the improper conduct of its supporters (crowd disturbances), the setting-off and throwing of fireworks and the display of illicit banners.
"In addition, regarding reports of alleged abuse directed at Czech Republic players from Russia fans, UEFA is investigating this further and is working with FARE to collect more evidence."
Denmark pulled off a big surprise on day two of Euro 2012 with a 1-0 win over hotly-tipped Holland.
In the second game of the evening, one goal from Germany's Mario Gomez was enough to see off Cristiano Ronaldo's Portugal.
The FARE (Football Against Racism in Europe) network has confirmed one of their observers at last night's Group A game in Wroclaw heard "fleeting" racist abuse of Czech Republic defender Theodor Gebre Selassie.
Asked if it included monkey chants, FARE chief executive Piara Powar told Press Association Sport:
"Our observer reported descriptions of that nature.
"It was directed at the Czech Republic's only black player."
UEFA asked FARE to help appoint expert spotters to report offensive banners, chants and behaviour in stadiums.
The London Fire Brigade has launched an advertising campaign in pub toilets to encourage fans to stop off for a takeaway rather than get a frying pan out after a few pints.
Latest ITV News reports
England coach Roy Hodgson has made his clearest statement yet on the reasons for leaving Rio Ferdinand out of his Euro 2012 squad.
The Russian Football Union has called for fan unity following the news that UEFA have opened disciplinary proceedings against Russia.