Mr Karleusa said more than 50 corpses - possibly of Kosovan civilians - were found in the refrigerated truck.
In particular, he said, Mr Milosevic had ordered the removal of evidence which would indicate the existence of civilian victims of the Serb repression of Kosovo Albanians in 1999.
Mr Milosevic and Mr Stojiljkovic have been indicted for war crimes in Kosovo by The Hague tribunal, but correspondents say this is the first time authorities in his own country have linked Mr Milosevic to war crimes allegations.
Corpse-filled lorry
The alleged cover-up was revealed during a police investigation into reports of a lorry filled with corpses that was dumped in the River Danube in 1999.
Mr Karleusa said more than 50 corpses - possibly of Kosovan civilians - were found in the refrigerated truck.
He said Mr Milosevic declared the case a state secret, preventing an investigation.
The former president and his key allies had discussed a "cleaning up of the terrain" in Kosovo, Mr Karleusa said.
He said Mr Milosevic had ordered his police to remove corpses "which could become the topic of possible investigation by the Hague tribunal".
Investigation
The truck has never been found and witnesses and news reports said that the bodies had been removed.
Police have so far discovered that the corpses were taken to an unknown location near Belgrade in two trucks.
"For now, it's clear that this was a case of removing evidence of criminal acts," said Serbian Interior Minister Dusan Mihajlovic.
The police are expected to file criminal charges once the investigation is completed.
Extradition
Human rights organisations and the UN tribunal have in the past accused Mr Milosevic of shipping the bodies of Kosovan civilians outside the province in a systematic attempt to cover up war crimes.
Jean-Jacques Joris, an adviser to the Hague's chief prosecutor Carla Del Ponte, said the police investigations make "clear that Milosevic was directly involved in the crimes committed in Kosovo".
If Yugoslav courts establish evidence of war crimes it could speed Mr Milosevic's extradition to face charges before the international tribunal.
The Yugoslav Government is preparing a new law, which would allow his extradition - a process presently barred by the Yugoslav constitution.
Mr Milosevic is currently in prison in Belgrade facing charges of corruption and abuse of power.