Both Poland and Ukraine said the claims, made in a BBC television documentary aired this week and in travel advice issued by foreign governments, did not give the true picture of the joint hosts of European football's premier tournament.
Former England captain Sol Campbell, who is black, warned fans to "stay home, watch it on TV... don't even risk it" after viewing footage of football fans in Poland and Ukraine making Nazi salutes and taunting black players with monkey chants.
The programme also uncovered anti-Semitism and a serious assault on a group of Asian students.
In Poland, organisers PL.2012 said the warnings were "unjust" and had "nothing to do with reality", adding that instances of xenophobia and racism in stadiums were "a problem specific to the whole of Europe and not only to Poland".
They went on to invite former Tottenham Hotspur defender Campbell to Poland to see for himself. "Get to know us as we really are," they added.
In neighbouring Ukraine, Euro 2012 organising committee chief Markiyan Lubyivskyi told reporters that Campbell was entitled to his own view and was sure it was not reflected widely in England.
"But we are hurt by it and fail to see what the point of these comments really is. I do not think it is dangerous for people of different ethnicity to come to Ukraine," he added.
Ukraine is already facing a potential boycott by top European Union leaders over the alleged mistreatment of the opposition leader and former prime minister Yulia Tymoshenko, who is in jail on what critics say are trumped-up corruption charges.
Lubyivskyi said media reporting the tournament should take a more balanced approach.
"I call on all media to declare a moratorium on negative information about the Euro. I would like to say that 80 to 90 percent of this information is false," he added.
Campbell's warning came after the families of two black England players -- Alex Oxlade-Chamberlain and Theo Walcott -- said they would not risk going to Ukraine to watch England's matches following public warnings from the British government.
"Although the vast majority of visitors experience no difficulties, foreign nationals have been the victims of violent crime in Kiev and other major cities," a Foreign Office statement in a fans' guide to the tournament read.
"In some cases, attacks have been racially motivated. Travellers of Asian or Afro-Caribbean descent and individuals belonging to religious minorities should take extra care."
The foreign ministries of Denmark and France have also issued similar warnings to fans about the risk of racist attacks.
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.