"In the days ahead, the attention of the world will be focused on our country. I urge you to show full Ukrainian hospitality, sincerity and friendliness," Yanukovich said in an address to the nation.
Ukraine, which is co-hosting the tournament with Poland, has suffered a deluge of bad publicity before the kick-off on Friday. Yanukovich made no reference to criticism from Western governments and media over the government's treatment of opposition leader Yulia Tymoshenko.
Many European Union politicians are threatening to boycott matches because of the jailing of Tymoshenko on a charge of abuse of office. Western governments say she is the victim of "selective justice".
"No ministers will be attending group games at Euro 2012," a foreign ministry spokesman said.
"We are keeping attendance at later stages of the tournament under review in the light of ministers' busy schedules ahead of the Olympics and widespread concerns about selective justice and the rule of law in Ukraine."
"Five years ago... no one believed that our country would have managed to prepare for the hosting of such a large-scale event," he said.
"We should correctly welcome guests and participants of the championship. The tourist future of our country will depend on how they remember Ukraine and Ukrainians," Yanukovich said.
