Video emerged Saturday of Russia fans fighting with stadium stewards in Wroclaw and UEFA also says it is investigating reports by anti-racism experts of abuse directed at Czech players during Russia's 4-1 victory.
In a statement posted on its website, the Football Union of Russia called on its large contingent of travelling fans to "Respect yourself, your home and your team."
The statement praised the majority of its fans for their boisterous support of the team but said political statements "have no place in the stands" and told supporters to co-operate fully with match organizers.
Friday's incidents flared before Russia takes on Poland in a highly charged Group A match in Warsaw on Tuesday — a Russian national holiday when fans plan to march from the city centre to the stadium.
The head of the Russian football union and the team's coach placed a wreath Sunday in Warsaw to honour the Polish president and 95 others killed in a 2010 plane crash in Russia.
The symbolic gesture came amid ongoing tensions between Poland and Russia based on a difficult history of war and occupation as well as new distrust that has emerged in the aftermath of the crash.
Sergei Fursenko and Dick Advocaat placed a wreath of pale pink roses at a plaque at the presidential palace in the Polish capital.
Anti-racist experts appointed by UEFA to monitor matches reported Saturday that fans verbally abused Czech defender Theodor Gebre Selassie, who is black.
UEFA's disciplinary panel will review the case against Russia — using "security reports and available images" — on Wednesday.
The alleged improper conduct relates to "crowd disturbances, the setting off and throwing of fireworks and the display of illicit banners," UEFA said.
Russia warned its fans not to throw fireworks, after the Czech Republic match was briefly held up while a steward removed a firework from the pitch.
"We understand your strong feelings and emotions in supporting the team and appreciate that you are so strongly rooting for us in the European Championship, but if this happens again the team could expect serious sanctions from UEFA, including the halting of the match and a technical defeat," the Russian football union said in a statement addressed to supporters.
It cited the example of Serbia, which missed a playoff spot in qualifying for Euro 2012 by a single point. Serbia's qualifier against Italy in Genoa was called off when fans threw flares and fireworks onto the pitch with the score at 0-0 and then clashed with police outside the stadium. UEFA awarded Italy a 3-0 win.
In Friday's incident, four stewards at the stadium were hospitalized and later discharged after being attacked by Russia fans, city police said.
Online footage showed fans punching the security staff in a stadium concourse area. One steward was punched to the ground and then kicked before the fans walked away.
Police and a witness who took video footage said the Russia fans became aggressive when stewards tried to capture a man who had thrown firecrackers toward the pitch.
Monitors from the Football Against Racism in Europe (FARE) fans' network reported to UEFA that Russia fans also displayed a nationalist "Russian Empire" flag.
The symbol was one "we take as evidence of far-right sensibilities," FARE executive director Piara Powar told The Associated Press.
Russian authorities urged fans to "realize that the success of the team is more important than any political or personal ambitions."
It also told them: "Don't succumb to provocations and help maintain order in the stadium. Root for us and not against someone. Help Russia win the tournament."
Friday's incidents are not the only ones to involve fans at Euro 2012.
Polish police said they had arrested 14 supporters involved in a brawl that broke out overnight ahead of Sunday's Group C match between Ireland and Croatia.
The fighting, which involved glass bottles and chairs being thrown, took place in the early hours of Sunday on the main square of Poznan.
Police detained 10 Poles, three Irish fans and one Croat, and were still trying to determine what role they had in the fight.
Associated Press writers Vanessa Gera in Warsaw, Karel Janicek in Wroclaw and Lynn Berry in Moscow contributed to this story.