"Dear Sol, feel invited -- feel like at home. In Poland, at our common Euro 2012. Get to know us as we really are," organisers PL.2012 said in statement on Tuesday.
On Monday, the former Tottenham Hotspur and England defender told a BBC television programme that fans should not go to the Euro 2012 amid fears about far-right gangs that have prompted the families of two black England footballers to stay away.
The families of Alex Oxlade-Chamberlain and Theo Walcott said they would not risk going to Ukraine to watch England's matches after public warnings from the British government.
The foreign ministries of Denmark and France have also warned fans about the risk of racist attacks.
In the BBC documentary, some fans at matches in both Poland and Ukraine were seen making Nazi salutes and taunting black players with monkey chants. It also uncovered anti-Semitism and a serious assault on a group of Asian students.
PL.2012, however, termed the warnings "unjust" and said they had "nothing to do with reality".
"The problem of stadium pathologies, such as xenophobia or racism, is a problem specific to the whole of Europe and not only to Poland," they added.
In an apparent bid to pre-empt football-related violence, police in Poland on Monday arrested 42 people -- including prominent members of football hooligan gangs -- suspected of being involved in drug trafficking and extortion.
Since the fall of the Iron Curtain two decades ago, the far-right has found fertile ground among fan gangs in Eastern Europe's football stadiums.
Monitors from the UEFA-backed Football Against Racism in Europe (FARE) network have recorded dozens of shocking far-right slogans at Ukrainian league matches and plan to deploy at Euro 2012 games.
But they said that the Euro 2012 spotlight has helped tackle the issue.
European football's governing body UEFA remains confident that Ukraine can ensure the safety of the 800,000 foreign fans expected at the tournament, which kicks off on June 8 in Poland.
Euro 2012 organisers hit back over racism fears
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