The Serbian government, which staunchly opposes Kosovo's move, is organising its May 11 parliamentary and local elections in Kosovo, where more than 115,000 Serbs have registered to vote.
Kosovo, where ethnic Albanians make up 90 per cent of the 1.8 million population, declared independence from Serbia on February 17.
Kosovo has been recognised by around 40 countries, including the US and most European Union nations, since its declaration.
"If there were no demonstrations against Serbia's elections ... then the world would have understood this as consent or weakness from Albanians and the path for the cantonisation of Kosovo would have opened," Kurti said.
"We are not against the Serbs here, we are against the structures of Serbia here."
The protesters also sprayed the Unmik buildings with sewage water.
The "self-determination" movement, which opposes the presence of the international community in Kosovo, also protested against Eulex, the European Union's incoming police and justice mission
UN and ethnic Albanian leaders are concerned that Belgrade may use the polls to strengthen a parallel Serbian administration at the local level.
Such a structure has remained since the 1999 war in the area, thanks to Serbia's political and financial assistance.
Leaders of the Kosovo Albanian government and Unmik have said that the local elections are illegal and that they will simply ignore the vote.
Speaking last week, Hajredin Kuci, Kosovo's deputy prime minister, said: "The Serbian elections are not legal and legitimate. But the government won't use any violence to stop them."