The European football federation UEFA says it has been informed that isolated racist incidents occurred as people watched a training session of the Netherlands team in Poland.
UEFA's statement came just before the Euro 2012 tournament was due to kick off in Poland and Ukraine.
The statement acknowledged reports of racist abuse of Dutch black players but said the association had not received a formal complaint from the Dutch team.
Earlier, the Netherlands' captain, Mark van Bommel, said some people who watched the training on June 6 in Krakow targeted the team's black players with "monkey" noises.
The incident has renewed concerns about possible racist behavior by fans as the tournament gets under way in Warsaw on June 8 with matches between Poland and Greece, and later, the Czech Republic against Russia in Wroclaw.
Van Bommel said the incident was particularly "disgraceful" as the team had just returned from a solemn tour of the German Nazi death camp at Auschwitz, near Krakow.
He said that if there was a repeat during a Euro 2012 match, the Dutch team would ask the referee to stop the game.
In its statement, UEFA said the association would have zero tolerance for any display of racism at the tournament.
In the wake of a recent BBC documentary highlighting racist behavior by Polish and Ukrainian football fans, officials in Poland and Ukraine have sought to dismiss concerns about potential racist abuse during the championship.
The Netherlands' training session in Krakow was watched by some 25,000 people. Krakow is not hosting any Euro 2012 matches.
The June 8-July 1 tournament is expected to draw hundreds of thousands of fans from across the world.
Numerous European officials have called for a boycott of matches in Ukraine in protest over former Prime Minister Yulia Tymoshenko's seven-year prison sentence on abuse of office charges they say are politically motivated.
The British government cited concerns about selective justice in Ukraine and said no ministers are expected to attend England's group matches in the country.
With reporting by AP and AFP