Fatmir Sejdiu called upon the opposition leader to lead the province's new government after his Democratic Party of Kosovo garnered 34 percent of the vote in elections.
Thaci, who needs to ally with other parties to govern, said he will begin a round of talks with various political parties, including the ruling Democratic League of Kosovo, which came second in the poll.
Officials from Thaci's party have said that a coalition between Kosovo's two largest parties is the most likely outcome of the negotiations to form a government.
Such a move would be hailed by Western diplomats who favor a broad political coalition seen as a guarantee of stability among ethnic Albanians as they move closer to the anticipated declaration of independence from Serbia.
A cabinet is expected to be named by the end of the month, although the province's assembly is not likely to convene to vote in the new government before January.
Thaci, 39, was leader of the now disbanded Kosovo Liberation Army that waged an independence war against Serbia in 1998-99. Most of his associates are former guerrilla leaders and are expected to take senior positions in the future government.
International envoys failed to resolve whether Kosovo should become independent or remain part of Serbia and the dispute will now go back to the U.N. Security Council where Russia, Serbia's ally, has threatened in the past to veto any measure that allows Kosovo to become a state.
The uncertainty has raised the stakes in Kosovo, with ethnic Albanians expecting a swift recognition of independence from Western capitals and minority Serbs threatening to leave the province and move to Serbia, or group in Kosovo's north where most of the minority lives and call for the territory to become part of Serbia.
Kosovo has been under U.N. administration since NATO bombed Serb forces in 1999 ending a brutal campaign against separatist ethnic Albanians.