The United Nations special envoy on Kosovo has met ethnic Albanian leaders at the start of his mission to mediate a deal on the province's future.
The ethnic Albanian team gave Martti Ahtisaari a document outlining their insistence on independence.
"The time has come to wrap up this business," Kosovo President Ibrahim Rugova said after the meeting.
Kosovo has been administered by the UN since Nato-led troops expelled Serb forces in 1999 to end the war there.
It is legally still a part of Serbia and Montenegro.
The UN Security Council appointed Mr Ahtisaari - a former Finnish president - to lead the talks process.
He made no comment after Tuesday's talks at Mr Rugova's residence.
Mr Ahtisaari was due to meet Serb religious leaders in the province later on Tuesday - as well as travelling to Belgrade and neighbouring countries.
He is expected to spend months shuttling between the Kosovo capital, Pristina, and Belgrade to reconcile their positions.
Kosovo's ethnic Albanian majority wants independence, but Serbia wants to maintain sovereignty over the province.
Before his arrival in Pristina on Monday, Mr Ahtisaari played down speculation that a deal might be reached in just three or four months.
However, he has also echoed the views of other UN officials who have said that the talks cannot be prolonged indefinitely.