Prime Minister Bajram Kosumi and the UN Civilian Administrator in Pristina, Soren Jessen-Petersen, were first to file past the body.
After them, the chief of the U.S. office in Pristina, Philip Goldberg came to pay his last respects to Rugova, who died of lung cancer in his Pristina residence last Saturday .
Braving freezing cold temperatures, residents of this UN-administered province started converging on Pristina on Monday morning to file past the body of the man whom they also call the father of their nation.
Citizens will be able to pay tributes in the parliament hall over next two days.
It was confirmed that the funeral will be held on Thursday, 26 January.
The committee in charge of preparation of funeral ceremonies decided to extend the period of mourning from five to fifteen days,
Schools are closed until Thursday.
On Thursday when the funeral is scheduled, state institutions, organisations and companies will not work in Kosovo.
Kosovo Assembly Chairman Nexhat Daci, who is acting president, told reporters on Sunday that many world leaders had confirmed their attendance at the funeral.
According to the local media, the arrival of the EU High Representative for Common Foreign and Security Policy, Javier Solana, and the UN chief negotiator in the talks on Kosovo's final status, Marti Ahtisaari, has been confirmed.
The local airport has started receiving requests for the landing of special planes carrying politicians from various parts of the world to Rugova's burial.
A great number of foreign reporters have arrived to cover the funeral of the 61-old Kosovo President.