Charles Zentai, 84, is alleged to have murdered Jewish teenager Peter Balazs in 1944.
Mr Zentai has denied the allegations brought against him by the Simon Wiesenthal Centre, an international Jewish human rights organisation, and is fighting the extradition.
The case was due to be heard in the Perth Magistrates Court in February.
But Mr Zentai - in tandem with alleged Irish fraudster Vincent O'Donoghue - initiated a Federal Court challenge against the power of West Australian magistrates to deal with commonwealth extradition laws.
Under federal law, extradition applications from foreign countries go before state magistrates, who assess their validity before referring them to the federal attorney-general for final adjudication.
Mr Zentai's lawyers argued there were constitutional problems with investing state judicial officers with powers to perform "executive" commonwealth roles.
They said the roles were incompatible because performing an "administrative function" for the commonwealth could damage the appearance of magistrates' judicial objectivity.
But Federal Court justice Antony Siopis has rejected Zentai's application saying there was no need for state legislation to allow magistrates to perform the commonwealth functions.
Mr Zentai is scheduled to appear in the Perth Magistrates Court on September 22.