Foreign Minister Bob Carr says the government has asked Israel for all information relevant to the arrest, detention and suicide of Australian-born Israeli spy Ben Zygier.
Zygier, who was reportedly jailed for passing secrets to Israel's arch-enemy Hezbollah in Lebanon, died in his prison cell in Israel in 2010.
Senator Carr says Australia will continue to have a dialogue with Israel about the case.
"I'm not aware that there has been a comprehensive accounting for what has happened. What gave rise to his arrest, his detention, his suicide," he said, wrapping up a week-long trip to the United States.
Israel says Zygier killed himself in what was meant to be a suicide-proof cell in a Tel Aviv jail.
His death in custody has focused attention on Israel's recruitment of agents with foreign passports.
Senator Carr says he maintains his concerns about Australian passports being used by Australians or dual citizens who are working for any intelligence agency.
"That would create risk for all Australians who are travelling," he said.
"So Australia's got a clear interest, a distinct point of view on this, an objection to Australian passports being used by dual citizens who are off working for a foreign intelligence agency.
"We have asked them for all information relevant to Australia on this and we will continue to do that."
Yesterday, Zygier has given highly sensitive information to an Eastern European man with links to Hezbollah while working for Israel's spy service Mossad.
Ronen Bergman, the intelligence correspondent for Israel's biggest selling daily newspaper Yedioth Ahronoth, published the report in Der Spiegel.
It claims Zygier started working for Mossad in 2003, and was employed to investigate European companies which were doing business with Iran and Syria.
It says Zygier - who was raised in Melbourne but moved to Israel about a decade before his death - was ordered back to Israel in 2007 because his bosses were unhappy with his work.
Bergman says, in an effort to save his career, Zygier then tried to recruit an Eastern European man linked to Hezbollah.
To prove himself, Zygier apparently gave him highly sensitive information, including the names of two Lebanese nationals working for Mossad.
The men, Ziad al-Homsi and Mustafa Ali Awadeh, were arrested in May 2009 on charges of spying for Israel and later jailed for several years.
Bergman says the Hezbollah contact "got the better of Zygier".
"So instead of obtaining information, Zygier was giving information," he wrote.