Charles Zentai, of Willeton in Perth's southern suburbs, turned himself in to police on Thursday and was taken to Hakea prison.

A 14-day stay on his surrender for extradition lapsed on Thursday after Zentai's family and lawyers said they would not appeal the decision by the full court of the Federal Court which dismissed his latest appeal against extradition.

The Hungarian government allege Zentai was one of three Hungarian soldiers who beat and tortured Jewish teenager Peter Balazs, before his body was thrown into the Danube River in Budapest in November 1944.

Zentai is now at the mercy of Mr O'Connor, delegated by Attorney-General Robert McClelland, to decide if Zentai should be extradited to face the alleged war crime.

A spokesman for Mr O'Connor said the minister would receive all the material relevant to the decision on Monday or early next week before considering it carefully and making a decision on the matter.

"He is required to do so as quickly as practical," the spokesman said.

Zentai has maintained his innocence since he was arrested in 2005 after a request to the federal government by Hungarian authorities.

He had used every available legal avenue to avoid extradition to his native Hungary but stopped short of seeking leave to appeal the latest Federal Court decision in the High Court.

Zentai's lawyer Denis Barich said Mr O'Connor would be able to consider his client's submissions under Section 22 of the Extradition Act, which set out constitutional arguments against his extradition.

Mr Barich says two fellow soldiers who had made allegations against Zentai in Mr Balazs' attack had not mentioned Zentai in their initial evidence to Hungarian authorities.

Mr Barich and Zentai's son Ernie Steiner both claim Hungarian authorities want Zentai for preliminary questioning about the matter, which could be done in Australia.

Mr Steiner said he had no trust in the Hungarian military court system, which Zentai would face if extradited.

"There are really important questions relating to their competency in being able to handle an issue like this and I would like the public prosecution in Hungary to explain how my father could receive a fair trial that conforms to international conventions," Mr Steiner told Fairfax Radio.

"How would it be possible to receive a fair trial in the absence of living witnesses?

"These are the statements being used against my father in trying to secure an extradition but he would have no opportunity to cross-examine these people and that in itself would be a travesty if it proceeded on that basis."

If the federal government orders his extradition, Zentai will be able to resume the legal appeals process, which is already believed to have cost him and his family about $200,000.

The Simon Wiesenthal Centre, a Jewish human rights group, have been persistent in their calls for Zentai's extradition to face the charge.

If Zentai is extradited he would be the first Australian citizen to be tried on Nazi war crimes.

Hungary was a German ally during World War II.

watoday.com.au