Bakir Izetbegovic, a member of Bosnia's tripartite presidency, said the appeal would be launched before a 10-year deadline expired on 26 February.
Bosnian Serb officials warned the move would trigger a new political crisis.
In 2007, the International Court of Justice (ICJ) cleared Serbia of direct responsibility for genocide.
The ICJ found only one act of genocide during Bosnia's 1992-95 war - the massacre of about 8,000 Bosnian Muslim (Bosniak) men and boys by Bosnian Serb forces in the town of Srebrenica in 1995.
