Charles Zentai is suspected of being one of three Nazi-backed Hungarian soldiers who tortured and murdered 18-year-old Jewish man Peter Balazs in November 1944 for not wearing a yellow Star of David.
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Hungarian-born Zentai, who has lived in Australia for some six decades and is an Australian citizen, has always maintained his innocence.
He was approved for extradition to Hungary in late 2009 but successfully appealed the ruling on the basis that a "war crime" was not an extraditable offence.
But Home Affairs Minister Brendan O'Connor has been granted leave to appeal the decision to the High Court, Australia's top judicial authority.
The court said Tuesday it would examine whether an alleged crime had to be an offence in the country in question at the time for extradition to be allowed.
Zentai's family has said the 90-year-old was willing to answer questions from Hungarian police about the murder but did not want to leave Australia to do so.
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