"I'm not aware that there has been a comprehensive accounting for what has happened," Foreign Minister Bob Carr was quoted as saying by the Australian news agency AAP.
"What gave rise to his arrest, his detention, his suicide?" he added.
"We have asked them for all information relevant to Australia on this, and we will continue to do that," he said.
Australian-Israeli Mossad agent Zygier was found dead in December 2010 in Israel's most secure prison cell.
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Carr said the government's dialogue with Israel was continuing.
"Australia has a clear interest, a distinct point of view on this - an objection to Australian passports being used by Australian citizens or dual citizens who are off working for foreign intelligence agencies," Carr said.
His comments come after the opposition yesterday called on Prime Minister Julia Gillard government to demand an immediate explanation from Israel as to whether Mossad misused Australian passports in its employment of Zygier, The Age newspaper reported.