Mr Zentai moved to Australia after WWII
The Australian Federal Court has ruled that an 88-year-old man can be extradited to Hungary to face accusations of murder.
Hungary's government accuses Charles Zentai of killing Jewish teenager Peter Balazs in Budapest in 1944.
At the time, Mr Zentai was a warrant officer in the Hungarian army, then allied to Nazi Germany.
Mr Zentai says he was not in Budapest at the time. He can still appeal to Australia's High Court.
The Hungarian government alleges that Mr Zentai took part in the fatal beating of Mr Balazs for not wearing a Star of David to identify him as Jewish.
The allegations against Mr Zentai were initially brought by the Simon Wiesenthal Center, a Jewish rights organisation dedicated to hunting down alleged Nazi war criminals.
He is listed as one of the centre's 10 most-wanted suspects, for having "participated in manhunts, persecution and murder of Jews in Budapest in 1944".
Mr Zentai moved to Australia after the war and was living in the western city of Perth when the Hungarian government began extradition proceedings in 2005.
A court ruled last year that he was eligible for extradition, a ruling upheld by a Federal Court judge on appeal. The full bench of the Federal Court has now upheld the extradition.
He has been granted two weeks to lodge another appeal, this time to Australia's High Court.
Mr Zentai's son, Ernie Steiner, said the family was considering its options.
"Obviously I am very concerned for my father, and I've had to ask him some very direct questions, and I'm convinced - through my own family history, statements he made in 1994 when my mother was still alive about the date of his departure from Budapest - he wasn't even there," Mr Steiner said.
The final say on Mr Zentai's extradition rests with Australia's Home Affairs Minister Brendan O'Connor, who has already invited submissions on the case.