Serbia have threatened to quit Euro 2024 if UEFA fail to take action following alleged chanting between fans of Croatia and Albania.
A section of supporters attending the 2-2 draw in Hamburg on Wednesday could be heard taking part in offensive chants aimed at Serbia.
Jovan Surbatovic, general secretary of the Football Association of Serbia, has suggested Serbia may not continue at the tournament in Germany unless the European governing body hands down sufficient punishments.
Serbia salvaged a 1-1 draw with Slovenia in their second Group C match on Thursday in Munich. Hours after the game, UEFA said it asked an in-house investigator to look at the allegations.
A disciplinary inspector was appointed, UEFA said, "to conduct an investigation regarding potential racist and/or discriminatory conduct by supporters that allegedly occurred."
UEFA gave no timeline for the case, which is unlikely to be resolved before Serbia's third and potentially last game -- on Tuesday against Denmark.
"What happened is scandalous and we will ask UEFA for sanctions, even if it means not continuing the competition," Surbatovic told Serbia state broadcaster RTS.
"We will demand from UEFA to punish the federations of both selections.
"We do not want to participate in that, but if UEFA does not punish them, we will think how we will proceed."
In a separate statement on Thursday, the Serbia FA condemned the "shameful racist behavior" of the Albanian and Croatian fans and said the match should have been suspended as soon as the chants started.
"Such insulting of a nation with cries that they should be killed has not been seen at sports events for a long time," the statement added.
UEFA president Aleksander Ceferin was with Serbian officials in Munich at the game Thursday against his home country Slovenia
On Wednesday, UEFA cancelled the media credentials of a Kosovar journalist Arlind Sadiku for allegedly making a nationalist gesture towards Serbia fans during their game against England in Gelsenkirchen on Sunday.
A statement issued by UEFA read: "UEFA can confirm that one journalist has had his accreditation cancelled due to misconduct at the UEFA EURO 2024 match between Serbia and England on 16 June 2024."
On Monday the Serbian Football Association was charged by UEFA after their supporters displayed a banner that "transmitted a provocative message unfit for a sports event" and for throwing objects inside the stadium.
That charge came after the Kosovo Football Federation complained to UEFA about "Serbian fans displaying political, chauvinistic, and racist messages against Kosovo" during their 1-0 defeat to England.
"We were punished for isolated cases and our fans behaved much better than the others," Surbatovic said.
"One fan was punished for racist insults and we don't want it to be attributed to others. We Serbs are gentlemen and we have an open heart."
Information from Reuters and The Associated Press contributed to this report