Prime Minister Donald Tusk warned that police were prepared to respond harshly to any violence.
"I hope we will not have to use force, but we will use it ruthlessly if necessary," Tusk said in an interview Friday on Radio Zet.
He said Russian President Vladimir Putin warned him that some Russians could try to get revenge for attacks against them Tuesday and that Russian authorities were also doing what they could do to control their hooligans.
The Russia soccer federation has appealed to its fans to show restraint and follow the UEFA rules of conduct.
The concerns centre around a Russia-Greece match in Warsaw on Saturday night, when more than 20,000 Russians are expected to be in Warsaw. The fears are that some of them could end up in street brawls with Poles.
Polish and Russian fans clashed Tuesday on the streets of Warsaw when their countries played. The game, one burdened by a difficult history between the two nations, ended in a 1-1 draw. In at least one case Polish hooligans attacked Russians, who fought back. The men kicked and beat each other and flares went off in their midst.
The fighting came as thousands of Russians marched to the stadium in a group, waving flags and nationalist symbols — viewed as a provocation by some Poles. One scuffle near the stadium was apparently started by Russians.
One of the worst cases of violence involved police firing rubber bullets and tear gas at young Polish men who attacked them with stones and bottles.
More than 200 people have since been arrested, Warsaw police spokesman Maciej Karczynski said Friday. Police had initially arrested 184 people, most of them Poles, but have caught more after studying security camera footage.
In other misbehaviour, Russian fans attacked stadium stewards at their team's first Euro 2012 match, on June 8 in Wroclaw. That prompted UEFA to fine the Russian soccer federation €120,000 ($150,000).
More than 20,000 Russians have tickets for Saturday's final group game with Greece in Warsaw, officials said. Another 3,000 Russians are expected to watch the game in public spaces, but no march is planned this time.
"We are aware that there is no shortage of cretins and there may be cases of behaviour of a provocative character on the Polish side, as well as on the Russian (side)," Justice Minister Jaroslaw Gowin told reporters Friday.
Courts have also convicted some of those arrested Tuesday in fast-track trials, though some ended up with only suspended sentences. Gowin was critical of the suspended sentences, saying he fears such leniency will only encourage further violence. Foreign Minister Radek Sikorski appealed Friday to the courts and prosecutors to deal decisively with "hooligan banditry."
Two Russians were among those found guilty of hooligan violence and they were immediately expelled from Poland, and will be banned from the European Union for five years, according to Ivetta Bialy, spokeswoman for Mazowieckie, the province where Warsaw is based.
Associated Press writer Monika Scislowska contributed to this report.Suggest a correction