Vasiljkovic's attorney, Bradley Slowgrove, told a Federal Court judge he was seeking a review of a finding - made in April by NSW deputy chief magistrate Paul Coran - that Mr Vasiljkovic was eligible for extradition, the daily said.
He also referred to two other matters before the Federal Court, one attacking the Extradition Act itself and the other seeking Vasiljkovic's release from jail.
The 52-year-old has been in Sydney's Parklea prison since his arrest in January 2006.
He is accused of killing Croatian civilians and instructing others to commit murder while he was a commander of Serbian paramilitary forces in Srpska Krajina during the Balkan conflict
from 1991 to 1995.
Vasiljkovic also is alleged to have fired on a civilian and kicked a person in the head.
He has repeatedly denied committing war crimes and his supporters say he is innocent, noting that the International Criminal Court in The Hague has not pursued him.
Vasiljkovic migrated to Australia with his mother when he was 12, returning to Serbia in 1991 to take command of a paramilitary unit.
His case is back in the Federal Court again on June 6