"Following the provision of new independent information today, regarding the two cases of alleged racist chanting in the Spain-Italy and Russia-Czech Republic matches, UEFA is now conducting further investigations," UEFA said in a statement.
"There are, however, no disciplinary proceedings opened at this moment in time."
Media reports said Italy striker Mario Balotelli was the victim of racist chanting during the Group C match against Spain in Gdansk on Sunday.
Czech Republic defender Theodor Gebre Selassie told reporters he had "noticed" racist chants directed at him in his side's opening Group A game with Russia in Wroclaw.
No official complaints have been made to UEFA by Italy or Czech Republic.
UEFA is on high alert for incidents of racism during the June 8-July 1 tournament.
The governing body wrote on Monday to the mayors of Polish and Ukrainian cities hosting Euro 2012 training sessions to ask for an increased police presence to avoid racist behaviour from fans.
Some members of the Netherlands squad complained of hearing monkey noises at an open training session at Wisla Krakow's stadium last week when tens of thousands of Poles turned up to watch.
The issue of racism dominated the build-up to the co-hosted tournament with a BBC documentary suggesting bigotry was widespread among fan groups.
Both Poland and Ukraine denied the allegations.
Before the tournament, the hot-headed Balotelli had warned he would "kill" anyone who threw a banana at him in the street during the European Championship.
In a separate case, UEFA has opened disciplinary proceedings against the Croatian Football Association for incidents during their opening Group C match against Ireland in Poznan on Sunday.
Croatian fans celebrated their second goal by letting off firecrackers and flares and a supporter dressed in his country's national team shirt came out of the stands and gave Croatia coach Slaven Bilic a kiss on the lips in front of the team bench.
UEFA said the Croatians have been charged with the setting off and throwing of fireworks and missiles, and invasion of the pitch.
