The United Nations chief negotiator for the final status of the UN-administered province in southern Serbia arrived in Tirana from Podgorica.
Top Albanian officials told him the status of Kosovo should reflect the will of the majority of its population, namely the province should become independent.
Apart from Moisiu, the Finnish diplomat also held talks with Prime Minister Sali Berisha.
After Tirana, Ahtisaari travels to Skopje, where he will meet Macedonian leaders and thus end the first round of negotiations about the future status of Kosovo in the region.