Draskovic asked the UN Administrator of Kosovo, Soren Jessen Petersen, to convey his sympathy to Rugova's family, Kosovo Parliament Speaker Nexhat Daci and Premier Bajram Kosumi, according to a Foreign Ministry statement.
Serbian President Boris Tadic also offered his condolences, saying that he respected Rugova as a politician and long-time leader of the Kosovo Albanians.
"I hope the death of Ibrahim Rugova will not hamper efforts to find a peaceful, compromise and negotiated solution to the future status of the province," Tadic said in his message.
Telegrams of condolence were also sent by Albania's President Alfred Moisiu and Prime Minister Sali Berisha.
Speaking to reporters in Tirana after an emergency government session, Berisha praised Rugova's contribution to the development of Kosovo and the promotion of good neighbourly relations between Kosovo and Albania.
The Albanian government said in a statement that the day of the burial of the Kosovo president would be declared a day of national mourning in Albania.