"We hope our police will be service-oriented and tolerant with fans. We have expressed this message many times to our colleagues in the Interior Ministry," Euro 2012 director Markian Lubkivsky said.
Ukraine, co-host of the tournament with Poland, expects at least 700,000 fans from around the world to attend matches in four Ukrainian cities - Kiev, Lviv, Kharkiv and Donetsk.
It will represent Ukraine's single biggest influx of foreign visitors since the former Soviet republic became independent 20 years ago.
Lubkivsky said that all games in Ukraine were assessed as "low risk" from a security point of view and organisers saw no likelihood of clashes among fans or soccer hooligans.
"We have not had any signals from police or from the state security service which give us cause to worry about security in the stadiums or in Ukraine," Lubkivsky said.
Altogether, Ukraine says it will have about 23,000 police on duty for Euro 2012, which runs from June 8 until the final in the capital Kiev on July 1. The first match in Ukraine is on June 9.
Human rights organisations have often accused Ukrainian police of using excessive force against suspects. Amnesty International has urged Ukraine to adopt legislation to put a brake on police violations during the Euros.
"As things stand, fans visiting Euro 2012 are under threat from a criminal police force," Max Tucker, Amnesty International's campaigner on Ukraine, said in a statement this month.
A fan group in Ukraine has warned foreigners to be cautious when confronting local police and allege that police used taser electric shock weapons against supporters in a league game in Donetsk this month.
"They (the police) have added a new feature to illegal detentions, fines, bans and police brutality. This new feature is electric shock torture ...," they said on their website.
"Ukrainian supporters have already been treated by the police in that way and Euro 2012 visitors are next in the line. So, dear guests, forget about your human rights - this is not Europe, this is Euro 2012!" they said.
Ukrainian police say they will guarantee order without resorting to violence.
"We will be loyal and will provide all help to our citizens and foreigners. We understand that the image of Ukraine also depends on us," police spokesman Volodymyr Polishchyuk said.