He has denied allegations that he was responsible for war crimes, including killings, against civilians and prisoners of war during the conflict in Croatia in the early Nineties.
Full reasons were to be published later for the June 15 decision by High Court judges to reject Vasiljkovic's appeal.
Barrister Brad Slowgrove, who has represented Vasiljkovic, told The Australian newspaper that there were still options open to the former paramilitary, including arguing that Croatia's extradition request does not conform to the Geneva conventions.
A hearing will be heard in Vasiljkovic's case in a Sydney court on July 12.