Warsaw authorities have appealed for calm ahead of a planned march by about 5,000 Russian fans to Warsaw Stadium to watch their team's Euro 2012 Group A match against Poland, which could be a potential flashpoint of the tournament.
The two neighbours have always had complicated relations, strained by historical animosity and the Soviet domination after World War II.
A plane crash that killed Poland's president and 95 others in Russia two years ago first brought the nations together, only to push them apart due to disputes over who was responsible.
Russian fans wanted to march to the stadium today and their representatives told Warsaw officials they wanted only to celebrate "the festival of football", the director of Warsaw's security and crisis unit said.
"I've asked them for peaceful behaviour, not to provoke anyone in the streets," said Ewa Gawor, in charge of security in Warsaw. "We want this festival to be peaceful. We've had such assurances, nevertheless we will be watchful."
UEFA has told Warsaw to expect about 20,000 Russian fans in the city, spread across the stadium and the fan zone. A Warsaw police spokesman said they were fully prepared, but declined to give precise numbers of how many officers would be on the streets.
Russia coach Dick Advocaat and the country's soccer chief laid a wreath in Warsaw on Sunday to commemorate the victims of the plane crash in an attempt to defuse tensions. A movement led by Jaroslaw Kaczynski, the ex-president's twin and leader of Poland's main opposition party, questions whether the crash was an accident and says Moscow may be at least partially to blame.
Poles also fear the Russian fans may display Soviet era symbols that remind them of the 44 years under Moscow's domination behind the Iron Curtain.
"Every little thing brings back all the historical grievances, which have not been fully resolved," said Andrzej Rychard, a sociologist at the Polish Academy of Science.
Alexander Shprygin, head of the Russian fan association, said: "Our walk has nothing to do with politics, fans have nothing to do with politics. All we want is to show support for our team - we don't want any provocations."
A group of Russian and Polish fans also laid wreaths together at a cemetery for Soviet soldiers and at the monument to the 1944 Warsaw uprising, Poland's PAP agency reported.
Russian fans displayed illegal banners and threw fireworks during the team's opening match against the Czech Republic in Wroclaw on Friday, and UEFA has launched disciplinary proceedings against the Russian FA, which has since appealed to its fans to behave.
Beyond isolated incidents, the tournament has so far been mostly calm.
Poland's interior minister said that, of 905,000 fans attending games at stadiums or in the fan zones, only 72 were arrested, including 41 local fans and 10 Russians.
Tensions are also growing between Russians and Ukrainians in the western Ukrainian city of Lviv, which hosts three Group B games. Russian fans scuffled briefly with Ukrainians outside the fan zone after the side's 4-1 win over the Czechs.
Lviv is in the western and predominantly ethnic Ukrainian part of the country, where Russians are identified with the Soviet control from 1939-91.
Mayor Andriy Sadovyi denied there were tensions, telling a news conference on Sunday; "We all have fun together - Russian, Ukrainians, Poles. I wish the same for other cities".
He said he wasn't planning extra police for the fan zone tomorrow and blamed Friday's problems on fans who had drunk too much beer.
Russian and Ukrainian nationalists exchanged blows in Lviv on May 9, 2011 during ceremonies to mark the end of World War Two. The trouble started when the Russians marched with a Communist flag.