Australia’s foreign minister on Wednesday ordered an investigation into his government’s handling of the 2010 detention and death of an Australian immigrant to Israel who was known as Prisoner X and may have been a spy, as Israel partially lifted a gag order that had prevented local journalists from reporting about the case.

n Australian news station reported on Tuesday that Prisoner X was Ben Zygier – known in Israel as Ben Alon – a 34-year-old father of two who had been in Israel for a decade before he was found hanged in a top-security prison cell where he had apparently been held secretly and denied visitors and a lawyer.

Australia’s Department of Foreign Affairs and Trade originally said in a statement early Wednesday that its embassy in Tel Aviv was unaware of Mr. Zygier’s situation until his family requested repatriation of his remains. A few hours later, another statement acknowledged that “some officers of the department were made aware” of his imprisonment beforehand “by another Australian agency.” The inquiry is into “the consular handling of this case,” according to the statement, with a preliminary report expected Thursday.

In Israel, members of Parliament and others called for inquiries into the mysterious case and the extraordinary secrecy surrounding it, including a court order that had forced the removal of news items from Israeli Web sites both in 2010 and again on Tuesday. Israeli journalists and politicians had protested that the media blackout was unreasonable in the Internet age, as the Australian news report circulated on social media, and on Wednesday it was modified to allow local publication of articles based on foreign reports.

Israeli Web sites quickly filled with photographs of Mr. Zygier and his grave in a Jewish cemetery in a Melbourne suburb. In addition to articles quoting extensively from the original Australian television report, there were many columns challenging the censorship policy and questioning the effectiveness of Mossad, the Israeli intelligence agency with which Mr. Zygier has been linked.

The prime minister’s office declined to discuss the case or the censorship of it.

Nitzan Horowitz, a member of Parliament from the left-wing Meretz Party, on Wednesday called on Israel’s attorney general to conduct “a complete and thorough inquiry” into “the circumstances of his imprisonment and, particularly, the circumstances of his death.” Speaking to Israel Radio, Mr. Horowitz said that when he inquired about Prisoner X after the 2010 reports, the attorney general’s office told him “that the matter was under supervision and under control and that everything was above board and that there was no such thing as a prisoner being held secretly.” Now, he said, “it seems that nothing about this was proper.”

“This is problematic for our democracy,” Mr. Horowitz said. “He died in prison, under the watch of the prisons service, an institution belonging to the state of Israel, and it was responsible for his safety. And we have to learn what happened there and how it happened.”

Rami Igra, a former high-ranking member of the Mossad, said such cases are more complicated than they seem, and that the detention might have been kept secret to avoid compromising other intelligence sources.

“The fact that this is not made public has a clear security reason behind it and is not something agreed to easily,” Mr. Igra said in a radio interview, noting the cost and effort it would take to keep a prisoner’s identity even from guards, as has been reported in this case. “Israel is a democratic, enlightened state, and there is no activity of the dark forces. What people are accustomed to see in the movies doesn’t exist in the state of Israel.”