The elected lawmakers "are responsible for the formation of a new government," said the joint statement issued on Friday from the embassies of the United States, Britain, France, Germany and Italy in Pristina.
Ramush Haradinaj, a former prime minister and an ex-rebel commander from the the Alliance for the Future of Kosovo (AKK) party, is the most likely candidate for prime minister.
However, his party holds only 39 seats in the 120-seat parliament and cannot create the new cabinet on its own.
Current Prime Minister Isa Mustafa's party, the Democratic League of Kosovo, has 23 seats, while the left-wing Vetevendosje opposition party has 32.
To form a government, Haradinaj either needs to create a coalition with another party or persuade individual lawmakers to support him.
Haradinaj served as the commander of the Kosovo Liberation Army during the 1998-1999 war with Serbia.
Serbia regards Haradinaj as a war criminal. However, the International Criminal Tribunal for the former Yugoslavia (ICTY) in The Hague has already tried Haradinaj twice and acquitted him of war crimes.
Mustafa called the snap elections in May after his government lost a no-confidence vote over accusations by the opposition that he had failed to deliver on his pledges for an improvement in Kosovo’s ailing economy.
Kosovo, a Muslim-dominated country in eastern Europe, which declared independence in 2008, is recognized by 114 countries.