The son of an 88-year-old alleged war criminal says his father is in good spirits having spent his first night in a prison in Perth.

Perth man Charles Zentai is accused of murdering a Jewish teenager in 1944.

Earlier this month the full bench of the Federal Court dismissed an appeal against his extradition to Hungary and Mr Zentai was taken into custody yesterday.

Mr Zentai's lawyers have indicated they will not be appealing against the Federal Court ruling, leaving the decision on his extradition with the Home Affairs Minister Brendan O'Connor.

Mr O'Connor says he will make a determination after he has considered representations made by both Mr Zentai's lawyers and the Hungarian lawyers.

Mr Zentai's son Ernie Steiner says his father is hopeful the Minister will make a speedy decision.

"We have trust in the Australian system," he said.

"It has its flaws but it's far better than sending my father to a military court in Hungary."

abc.net.au