The federation of Serbia and Montenegro has failed to approve a new national anthem in time for the Olympic Games.
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A special session of parliament postponed an emergency vote on the issue until at least September.
Since the break-up of Yugoslavia in 2002, Serbia and Montenegro has used the old Yugoslav anthem.
On Tuesday, the head of the Serbian Orthodox church denounced the new tune - a hybrid of an old Serbian song and a new Montenegrin one - as a "centaur".
Following the criticism from Patriarch Pavle, an opposition party from Montenegro decided not to support the proposed anthem.
"What influenced us not to vote for the urgent procedure is the moral weight and the importance of the Patriarch's person," the Montenegro Socialist People's Party Zoran Zizic said, according to Reuters.
The proposed new anthem combines elements of the Montenegrin anthem and one used by Serbia before World War II.
The Montenegrin anthem was recently adopted by Montenegro's parliament, along with its own flag and national day, as part of a push for the republic's independence from Serbia.
The old Yugoslav anthem, Hej Slaveni, used for more than 50 years, is popular among older generations, but it is regularly booed by the young when played at sporting events.