Zygier worked for Israel's spy agency Mossad before his death in an Israeli jail in 2010.
Foreign Affairs Minister Bob Carr says an internal report by the Department of Foreign Affairs (DFAT) has highlighted problems with the way the case was handled and admitted it was possible Australian passports were used by foreign governments for intelligence purposes.
The report into Zygier's death says former foreign affairs minister Mr Smith was on the distribution list for two ministerial submissions about Zygier's detention.
However, the report also notes there is no evidence the submissions were drawn to Mr Smith's attention.
Mr Smith, who is now the Defence Minister, says he does not recall them.
Opposition foreign affairs spokeswoman Julie Bishop says if that is the case, there must have been a serious breakdown in the minister's administration of his office.
Ms Bishop says Mr Smith must make a public statement to explain why the matter slipped through the cracks.
"He claims to have no recollection of it or that his department didn't brief him on it or his office. That just beggars belief," she said.
"It means there's been a massive breakdown in communications and the administration of the then-foreign minister's office.
"He needs to explain how it is he could have no recollection of being briefed on a matter involving an Australian citizen detained in Israel, national security, secret intelligence. It's just extraordinary," she said.
Mr Rudd held meetings with Israeli prime minister Benjamin Netanyahu just days before Zygier died.
Mr Rudd says he has no recollection of being briefed on the case.
"That our ambassador to Israel was not made aware of this case until after Mr Zygier's death is of concern. The report acknowledges that in hindsight DFAT should have done this," a spokesman for Mr Rudd said.
"That the then foreign minister Smith was not briefed on this as a consular matter is also of concern."
One of the major questions left unanswered is what exactly Zygier was charged with.
But a leading Israeli journalist on security and intelligence affairs says the Australian Government knows what charges Zygier was facing.
Yossi Melman says the Government knows much more than it is telling the public.
"I think that the Australian Government already knows what were the charges against him," he said.
"I have a feeling from reading the reports published today in Australia that the Australian Government knows much more than it is ready to reveal to the public."
Mr Melman says that Australia's intelligence services have a good relationship with Mossad, and it is likely the Israeli spy agency and the Australian Security Intelligence Organisation (ASIO) were "in constant touch".
"There is a good cooperation and liaison relations between our Mossad and your foreign spy agency," he said.
"I have a feeling that your security services - at least the security services - were in constant touch with the Israeli security services.
"[I think] your security services know slightly more about the operational side, which can explain what he was doing, why he was arrested, was he accused of treachery or just espionage or a contact with a foreign agent, but they don't tell it."
The circumstances surrounding Zygier's death, revealed by ABC's Foreign Correspondent report last month, raise the possibility of Australian passports being used by Israeli authorities in connection with the assassination of Mahmoud al-Mabhouh in Dubai in 2010.
The airing of the allegations has strained the Federal Government's relations with Israeli, which went to extraordinary lengths to prevent the release of details about the case.
But Mr Melman doubts Zygier was locked away to prevent him telling the Australian Government about the misuse of the passports.
"I don't buy it," he said.
"Maybe he used a different cover, but even if he used his Australian identity or one of the identities which he took from Australia, still from the Israeli point of view he was an Israeli operative working for the Israeli security services."