Hashim Thaci spoke after meeting in Pristina with Ilir Bytyci, brother of Ylli, Mehmet and Agron Bytyci, whose bodies were found in a mass grave in Serbia in 2001.
Thaci said Bytyci's killers "are positioned at the highest institutions of the state of Serbia," pledging Pristina will increase pressure to clarify the circumstances of their deaths and bring the perpetrators to justice.
"The names of the murderers of Bytyci brothers are known," said Thaci.
Washington has linked a former Serbian police commander, Goran Radosavljevic, known as Guri, to their killing and has banned him and his family from entering the United States.
Radosavljevic has denied involvement.
The Bytyci family has accused Serbia's authorities of refusing to bring the killers to justice though President Aleksandar Vucic has repeatedly promised to solve the case.
The brothers left their New York pizza business to fight with ethnic Albanian fighters against Serbia's rule in Kosovo. They were arrested at the end of the clashes in 1999 when they strayed into central Serbia.
Their bodies, with bullet holes in the back of their heads, were thrown into a pit that already held dozens of corpses of slain ethnic Albanian civilians.
Kosovo's 1998-99 war for independence ended with a 78-day NATO air campaign. The U.N. then ran Kosovo until its 2008 declaration of independence, which is recognized by 116 countries, but not by Serbia.
Some 10,000 people died and 1,660 remain missing.
Copyright 2019 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.