The two constituent republics of Serbia and Montenegro have fallen out over what colours should be used in the new state's flag.
An official from one of Montenegro's ruling parties described as "unacceptable and inappropriate" plans to use the Serbian tricolour.
Use of the Serbian flag could upset Montenegrins
Branislav Radulovic told the Vijesti daily that a completely new flag should be created which "fully reflects the meaning of the state union".
The Serbian and Montenegrin republican flags differ only in their shades of blue - dark and light respectively.
In each case the blue horizontal bands are sandwiched between red and white.
Montenegro's flag has a different shade of blue
"Not only is this proposal inappropriate and symbolically violating the essence of the union as a union of two historic states, it also demonstrates unconcealed arrogance," Mr Radulovic said of the proposal.
He suggested a compromise solution involving two vertical strips - red for Montenegro and blue for Serbia.
The new state replaced Yugoslavia in February, and its parliament is expected to pass legislation on a new flag, anthem and national symbols by the end of the year.
Democratic Opposition of Serbia (DOS), the republic's ruling party, said the Serbian flag should be used as it was already to all practical purposes the flag of the new state.
But the move appears to have deeply upset many Montenegrins, who are heavily outnumbered by Serbians in the new country.
Montenegrin leaders have been increasingly keen for independence since the fall of former Yugoslav President Slobodan Milosevic in 1999, but have now shelved plans under the new union agreement.
Serbia and Montenegro currently uses the horizontally stripped blue-white-red flag of the old Yugoslavia.
But the flag dates back to the creation of the Kingdom of Serbs, Croats and Slovenes - Yugoslavia's forerunner - after World War I.
It acquired a red star when Josip Broz Tito came to power in 1945, but lost it again when the old Yugoslavia fell apart in the early 1990s.