Many Poles were angered by a British TV documentary which showed racist and anti-Semitic violence at stadiums in Poland and co-hosts Ukraine. Former England international Sol Campbell warned fans to stay at home or risk coming back in a coffin.
Polish and Ukrainian officials say the report was one-sided and focused on the worst elements among the supporters of local clubs.
"Poles are fully prepared for their role as hosts," Prime Minister Donald Tusk said after a lunch of lamb and yams with the family of John Godson, a Nigerian-born politician who has lived in Poland for nearly two decades.
Sporting an English fans' lapel pin with the word "Welcome!", Tusk added: "I invite all English fans to come to Poland. Nothing unpleasant will meet you here. We will pass the hospitality test."
Poland has cracked down on hooliganism after several violent incidents at stadiums over the last year. Last month, police arrested suspected ringleaders of hard-core fan groups with ties to the drugs underworld.
Hooliganism surfaced as an issue in last year's general election and Tusk remains a target of insults by some hard-core supporters groups. He was heckled by several young men in front of Godson's apartment block in the central city of Lodz.