The assembly consists of 43 Serb representatives elected in Serb local elections in Kosovo, held in May.
"The assembly is the foundation of the Serb protection of Kosovo," said Marko Jaksic, one of the hardline Serb leaders. "We will not allow the formation of another Albanian state in this part of Europe."
Kosovo's President Fatmir Sejdiu has said that the Kosovo Serb leaders are trying to destabilize the new country by creating a separate assembly. He said the self-proclaimed parliament is part of their "illegal structures."
Creation of the new assembly is likely to further raise tensions between the Kosovo Albanians - 90 percent of Kosovo's 2 million people - and the Serb minority. Their rivalry has brought the fledgling state to the verge of partition.
The Serb representatives met as they marked Vidovdan, or St. Vitus Day - the anniversary of the 1389 battle in which a Christian army led by Serbian Prince Lazar was defeated in Kosovo by the invading forces of the Muslim Ottoman Turks.
The battle came to symbolize Serbs' historic resolve not to give up Kosovo, the heartland of their statehood and religion.
Kosovo police strengthened security and divert traffic away from Serb enclaves throughout Kosovo to prevent clashes with ethnic Albanians as Serb pilgrims visited the site of the battle.
Kosovo declared independence from Serbia in February, and has since won recognition from the U.S. and most EU nations. But, Serbia and Russia have declared the move illegal under international law. Kosovo's constitution came into force on June 15, granting broad autonomy to the Serb minority in Kosovo.
Kosovo's Serbs have largely shunned the new country's institutions, in line with Belgrade's instructions to undermine the government and international mentors and to work directly with Serbia instead.
The U.N. had planned to leave once Kosovo's authorities took control, alongside a European Union mission, after the constitution came into effect.
Following Russia's objections, which blocked the deployment of the EU mission, the U.N. was forced to remain and deal largely with issues concerning the Serb minority.