Kosovo's parliament is to meet at noon (11:00 a.m. GMT) on Sunday, and an official declaration of unilateral independence is widely-expected to follow. The U.S. and many European countries have said they are ready to recognize Kosovo.
Crowds were also gathering in other cities across the province, which has a population of some two million. There were fears, however, that ethnic clashes could break out between Serbs and ethnic Albanians.
Kosovan Prime Minister Hashim Thaci said on Saturday that, "The success of Kosovo's independence as a new beginning will be clearly measured by respect for the rights of minorities, especially Serbs."
NATO peacekeeping troops are on alert, ready to deal with any clashes between ethnic Albanians and Serbs in the flashpoint town of Mitrovica, in northern Kosovo.
U.S. President George Bush, currently on a week-long tour of Africa, said in Tanzania that, "The United States will continue to work with our allies to the very best we can to make sure there's no violence."
"We are heartened by the fact that the Kosovo government has clearly proclaimed its willingness and its desire to support Serbian rights in Kosovo," he went on.
Belgrade has ruled out the use of force to prevent the breakaway of Kosovo.
Serbia's ally, Russia, remains deeply opposed to any unilateral declaration of independence by Kosovo, saying that it would contradict international law, and would set a dangerous precedent for other secessionist regions.
"We are speaking here about the subversion of all the foundations of international law, about the subversion of those principles which, at huge effort, and at the cost of Europe's pain, sacrifice and bloodletting have been earned and laid down as a basis of its existence," Russian Foreign Minister Sergei Lavrov said on February 12.
Russia has hinted that it may now recognize Georgia's breakaway regions of Abkhazia and South Ossetia.
"The declaration of sovereignty by Kosovo and its recognition will undoubtedly be taken into account in [Russia's] relations with Abkhazia and South Ossetia," the Russian Foreign Ministry said in a statement on Friday.
South Ossetia and Abkhazia declared independence from Georgia following bloody conflicts in the wake of the Soviet Union's 1991 collapse.
The European Union gave its final approval for sending a civilian and police mission to Kosovo to replace the current UN mission, diplomatic sources in Brussels said on Saturday.
Kosovo has been a UN protectorate since the NATO bombing of the former Yugoslavia ended a conflict between Albanian and Serb forces in 1999.