UEFA handed out a punishment for offensive chants and disorder following an incident involving Croatia fans in 2023.
It emerged on Thursday that Serbia are threatening to pull out of this summer's European Championship.
Dragan Stojkovic's side, who lost their Group C opener against England on Sunday, are scheduled to face Slovenia at the Allianz Arena in Munich on Thursday afternoon.
But their future at Euro 2024 is now in the air after Serbia claimed that fellow Balkan nations Croatia and Albania fans chanted "kill, kill, kill the Serb" during Wednesday's 2-2 draw in Hamburg.
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Jovan Surbatovic, the General Secretary of the Football Association of Serbia, has submitted a request for UEFA to punish both Croatia and Albania for the alleged chants in the 59th minute.
In fact, he has warned that Serbia are ready to walk away from the competition if no action is taken.
"First of all, I want to thank our fans for their support in the match against England and I hope we will beat Slovenia," he told via RTS.
"What happened is scandalous and we will ask UEFA for sanctions, even if it means not continuing the competition.
"We are sure that they will be punished, because they have already responded to our appeal to remove the so-called journalist from Albania from the championship."
Surbatovic added: "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 will we proceed.
"We were punished for isolated cases and our fans behaved much better than the others. 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, so I appeal to the fans to remain gentlemen."
Serbia would likely be handed a huge fine if they did walk away from the tournament.
UEFA previously handed out a $165,000 (€150,000) fine to Croatia’s football federation for offensive chants and disorder by fans at the Nations League Finals in 2023.
They said its disciplinary panel combined incidents during games against the Netherlands and Spain at the tournament.
In total, a $77,000 (€70,000] fine was handed out for “discriminatory behavior” by fans, and other fines were given for throwing objects and lighting fireworks.
Jack Kenmare