The Prisoner X - identified by Australian media as Ben Zygier - apparently hanged himself in a prison near Tel Aviv in 2010.
Foreign Minister Bob Carr said his department was in a process of compiling a report on the case and has asked Israeli government about some information.
"We have asked the Israeli government for a contribution to that report," he was quoted as saying.
"We want to give them an opportunity to submit to us an explanation of how this tragic death came about."
Earlier, Carr ordered a review of the Zygier case in a bid to find that enough was being done by Australian consular staff and to identify any potential areas for improvement.
'The Australian' report quoted Attorney General Mark Dreyfus as saying he does not see the need for such a review.
Dreyfus said that he was confident that the Department of Foreign Affairs and Trade would get to the bottom of what he described as a "family tragedy".
"I haven't seen any need either for such a review to take place within the Attorney-General's department," Dreyfus said.
Zygier was arrested by Israeli authorities in February 2010 and was held in a maximum security cell under a false name until he died in December 2010.
The Australian government's handling of the Zygier case has come under scrutiny after confusion over who knew about his arrest and detention.
Melbourne: Australia has asked Israel to provide information about the death of Prisoner X, a jailed Australian-Israeli with links to spy agency Mossad.
First Published: Monday, February 18, 2013, 12:04