The prosecutor's office said the investigation would look into three separate alleged war crimes when two people went missing and two others were seriously injured and robbed.
The prosecution statement added that the violations of international law took place near the western Kosovo towns of Pec and Djakovica, in March and June 1999.
The victims were Serbs, ethnic Albanians and Gypsies, or Roma, the statement said, providing no other details.
There was no immediate comment from Kosovo, which has been run by a United Nations administration since the 1999 war.
The province has formally been a part of Serbia, but Belgrade has had no authority over it since the 1999 Nato attacks forced the then president, Slobodan Milosevic, to end a crackdown against Kosovo Albanian separatists and pull out the Serb troops.
About 10,000 people, mostly ethnic Albanians, were killed during the Kosovo war.
But the rebel KLA troops have also been accused of kidnappings and killings of hundreds of Serbs and other non-Albanians during the conflict and after the pullout of Serb troops in 1999.
Meanwhile, in a separate development a US envoy has urged Belgrade officials to play a "constructive role" in ongoing talks over Kosovo's future states, as Serbia said it would soon come up with a specific proposal for the autonomy of the UN-run province.
Frank Wisner, who is the US representative in the UN-brokered negotiations on the future status of Kosovo, met Serbian leaders as part of a tour of the region that also included visits to Kosovo and Macedonia.
Wisner met Vojislav Kostunica, the prime minister, Boris Tadic, the president, and Vuk Draskovic, the foreign minister.
It was hoped that the visit would restart UN efforts to negotiate the final status of the province, home to two million people.
Kosovo's ethnic Albanian majority insists on independence, while its Serb minority and Belgrade are seeking to keep Kosovo at least formally within Serbia's boundaries.