Prime Minister Julia Gillard says the government has learnt lessons from the shadowy case of suspected Israeli spy Ben Zygier.

Foreign Minister Bob Carr criticised the Department of Foreign Affairs and Trade's handling of the case after an internal report found it did not pass on news of Mr Zygier's arrest to the right people or proactively seek to offer him consular assistance.

The report shows the offices of then-prime minister Kevin Rudd and then-foreign minister Stephen Smith were told about Mr Zygier's arrest in early 2010 but both men say they cannot remember ever being personally briefed about it.

Ms Gillard spoke about the report for the first time on Thursday.

"What that report shows is there could have been better work between ASIO and the Department of Foreign Affairs and Trade on Australia actively, pro-actively, engaging in consular work with this young man," she told reporters in Sydney.

"As it was, the family never requested consular assistance, but I think we've learned some lessons about protocols for working when people are detained on issues associated with intelligence."

But the opposition and the Australian Greens say the government still has questions to answer over the affair.

Greens leader Christine Milne wants to know whether Senator Carr has sought the judge's report from the Israeli government on the circumstances surrounding Mr Zygier's death in mysterious circumstances in December 2010.

"When will Minister Carr pursue the Israeli government on these matters? And when will Stephen Smith come clean on what he was told at the time by his own department, and whether or not he told then-prime minister Rudd what was going on."

Senator Carr ordered the internal investigation last month after Mr Zygier was named as Israel's mysterious "Prisoner X".

The dual Australian-Israeli citizen was detained for alleged Israeli national security offences and died in a supposedly suicide-proof cell in December 2010. It's believed he worked for Israeli spy agency Mossad.