Currently, minorities have this privilege in areas where they make up at least 30 percent of the population. Croatia's liberal government has said no change is needed, insisting that the existing law complies with standards of the European Union, which Croatia joined in July.
Nationalists in the eastern town of Vukovar, the hardest hit area during the Serb-Croat war in the 1990s, have pulled down official signs there that were written in both the Latin alphabet of Croats and the Cyrillic one of Serbs.
On Friday, the nationalists said they have collected the 650,000 signatures required for a national referendum proposing to change the law so that a minority would have to make up at least 50 percent of a town population to have that language privilege.
Serb leader Milorad Pupovac warned that the initiative already has fueled ethnic tensions stemming from the 1991-95 war. He said, "Unless steps are taken to stop this, tensions and conflicts will go on."
Croatian Prime Minister Zoran Milanovic has said minority rights cannot be questioned in a referendum.
More than 10,000 people died during the Croatian war, which erupted when the country declared independence from Yugoslavia and minority Serbs rebelled against the decision.
Since becoming an EU member, Croatia has seen a strengthening of nationalist and conservative groups, largely fueled by joblessness and economic hardship.