The head of the Serbian football association threatened to pull the team out of the European Championship over chants made during Wednesday's draw between Albania and Croatia.
Jovan Surbatovic, the General Secretary of the Football Association of Serbia (FSS), told Serbian broadcaster RTS that the country demanded action from authorities over remarks made during the match, including the chant: "Kill, kill, kill the Serb".
Surbatovic told RTS the FSS would seek sanctions from Uefa "even at the cost of not continuing the competition."
Meanwhile, Uefa, the governing body of European football, said it has opened a probe into the matter.
An ethics and disciplinary inspector has been appointed to "conduct an investigation regarding potential racist and/or discriminatory conduct by supporters" during the match, a statement said.
A probe has also been opened in "relation to the alleged inappropriate behaviour of the Albanian Football Association (FSHF) player Mirlind Daku", the statement added.
Serbian media reported that Daku initiated vulgar chants against Serbs and Macedonians.
The Football Federation of Macedonia (FFM) condemned Daku's "nationalist chants" and announced an official letter to Uefa over his "scandalous behaviour".
The federation in a statement called on Daku to "publicly apologise for his behaviour".
Late Thursday, Daku asked for forgiveness from those he had offended, arguing that the "effect of the game takes its toll".
"I feel a moral and professional obligation to do so, for all those who have been hurt," he said on Facebook.
Serbia coach Dragan Stojkovic said the chants issue was "not important" after his side's 1-1 draw with Slovenia on Thursday kept them in contention for the next round.
"Please ask me about the game. For me this is not important, I'm just focusing on the game," he told reporters.
"Honestly, I didn't read anything. Believe me or not, but it's true."
Serbia has had tense relations with both Albania and Croatia in past decades.
In the 1990s, a string of wars broke out across the former Yugoslavia that saw bloody fighting in Bosnia, Croatia and Slovenia.
Many blamed late Serbian president Slobodan Milosevic for instigating the conflicts.
Serbia also fought a war against ethnic Albanian insurgents in the breakaway province of Kosovo in the late 1990s, which triggered a NATO intervention in the conflict.
Serbia are competing in their first European Championship since the dissolution of Yugoslavia.
They lost 1-0 to England in their opening match.