The neighbours, who will share matches between 16 countries throughout June leading to a July 1 final in the Ukrainian capital, moved to counteract a BBC Panorama investigative programme on football violence filmed in their countries.
The programme, aired on Monday, contained footage of fans giving Nazi salutes, taunting black players with monkey noises, anti-Semitic chants and a group of Asian students being attacked at the Metalist Stadium in Kharkiv, one of the four Ukrainian cities which will be hosting group matches.
Polish Prime Minister Donald Tusk said: "Nobody who comes to Poland will be in any danger because of his race."
"This is not our custom, as is not pointing out similar incidents in other countries, although we know they take place. In Poland, they're a rarity," he told a news conference in Rome.
In Kiev, Ukraine's foreign ministry went further, saying the allegations were a "dreamed up and mythical problem".
"You can criticise Ukrainian society for a lot of things... but, in the practice of racism, European Union member countries are a long way ahead of Ukraine," said ministry spokesman Oleh Voloshyn in comments reported by Interfax news agency.
Reports of high-level corruption, excessive hotel prices, violence against participants of a Gay pride meeting and graphic images of a brawl among law-makers in parliament over a language law have further damaged Ukraine's international image.
Campbell, who played 73 times for England and appeared at six major tournaments, said: "Stay at home, watch it on TV. Don't even risk it... because you could end up coming back in a coffin."
Ukrainian players rallied to their country's defence.
Striker Andriy Shevchenko, who formerly played for the English club Chelsea, said: "We do not have any real problems with racism here. Ukraine is a very peaceful country and people here are very friendly. I know that everything will be done for Euro 2012 to take place at a high
