"We have sold 95 percent of tickets for the Euro 2012 games," UEFA operations director Martin Kallen told reporters in the Ukrainian capital.
"We will additionally sell 50,000 tickets as not all (national) federations have used their quotas. Prices will not go up, they will be the same."
Kallen said tickets were still available for games in three Ukrainian cities - Kiev, Donetsk and Kharkiv.
Earlier this month, UEFA president Michel Platini warned Ukraine, who are jointly hosting the championship with Poland, that fans would snub matches in the former Soviet republic unless it brought down hotel prices which he said had been hiked up by "bandits and swindlers".
The government has responded by launching anti-trust investigations against hotels and promising a quick deal with low-cost airline Ryanair.
Euro 2012 runs from June 8 to July 1.