The main hearing will commence before the Hague-based ICJ on Monday, following Bosnia's suit against Belgrade accusing it of aggression and genocide in the 1992-1995 war.
The rallies pooled thousands of demonstrators in Sarajevo, Tuzla, Zenica, Cazin, Mostar and Gorazde, according to estimates of the rallies' organisers, associations of Bosniak (Bosnian Muslim) war veterans and families of the dead soldiers and civilian victims.
Serb representatives in the Bosnian government continue to challenge whether the lawsuit is justified.
A final verdict is expected to be delivered by the end of this year.