Five days of mourning were proclaimedafter Mr Rugova, 61, died of lung cancer on Saturday, leaving a vacuum which has raised fears of political turmoil in the disputed province.
Thousands of ethnic Albanians lit candles, placed flowers, raised flags at half mast and formed long lines to pay condolences at his hillside official residence, as they mourned the man who symbolised the 16-year old campaign for independence from Serbia.
Mr Rugova was known as the "Gandhi of the Balkans" because of his strategy of peaceful resistance. But his death occurred at a delicate moment for Kosovo, with the issue of the province's status to be discussed at UN-sponsored negotiations with Serbia on Wednesday. The talks have been postponed until February. The major powers have signalled they want a decision on status this year. Serbia says Kosovo is the cradle of the Serb nation and can never become independent.
The UN administration called for calm, fearing that less moderate politicians will trigger a leadership crisis. "The aim to which he dedicated his life is that of a free Kosovo," the UN administrator Soren Jessen-Petersen told a commemorative session of parliament yesterday. "It is a vision whose realisation remains in the hands of you, Kosovo's political leaders, whose unity and commitment to Mr Rugova's mission will be vital in the coming months."
Mr Rugova, who was twice elected president, did not cultivate a successor within his Democratic Alliance of Kosovo Party.
His civil disobedience campaign against the regime of Slobodan Milosevic, launched in 1990, was undermined by young, aggressive leaders who started an armed rebellion against Belgrade in 1998.
These power-hungry figures are now leading the game. Among them is Hashim Thaci, 37, the leader of dismantled Kosovo Liberation Army and the armed rebellion. Many ethnic Albanians consider him a war her. Another contender is Veton Surroi, 43, owner of the Koha Ditore newspaper and KTV television. He was an outspoken critic of Belgrade's repression of the province's ethnic Albanian majority.
The extreme repression of Mr Milosevic's regime led to the Nato bombing of Serbia in 1999. The UN administration took over after the end of the campaign and Kosovo began building its own democratic institutions.
For now, the post of president goes to Nexhat Daci, 61, a Rugova ally and speaker of Kosovo's parliament. In accordance with the constitution, he will remain acting president until a leader is elected within the next three months.
The death of Mr Rugova - whose trademark was a red scarf that he wore as a souvenir of his years in Paris studying for a doctorate in literature at the Sorbonne - marks the end of an era in Kosovo. Many Kosovans believe little progress would have been achieved without him.
Kosovans can pay their last respects to Mr Rugova, whose body will lie in state today and tomorrow in the parliament in the provincial capital, Pristina, before Thursday's burial. But the battle for his succession will be uppermost in mourners' minds.