Ban made his appeal after talks in The Hague today with the chairman of the International Criminal Tribunal for the former Yugoslavia and its chief prosecutor, Carla Del Ponte.
He said it was "crucial for international peace and prosperity" to end the impunity of indicted war criminals.
Both men have been indicted for genocide during Bosnia's 1992-95 war.
In a separate development, Bosnia's war crimes court today indicted a Bosnian Muslim wartime commander for instigating the killing of Croatian Serb soldiers.
Sefik Alic, 38, was arrested in November after he was recognized in an amateur video that showed ethnic Serbs fleeing Croatia after Operation Storm, a Croatian Army offensive in August, 1995.
The court said Alic participated in the "physical and mental abuse" of four Croatian Serb prisoners of war, who were later killed by soldiers under his command.