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The statement by Prime Minister Benjamin Netanyahu's office, which oversees Israel's intelligence services, was the first to confirm the affair concerned Ben Zygier, who was named in an Australian TV expose last week.
One of Zygier's lawyers has since linked him to Mossad, fanning speculation the 34-year-old Jewish man from Melbourne had been arrested and held in isolation on suspicion of betraying the Israeli spy agency's secrets - perhaps to Australia.
"Following many reports, the prime minister's office emphasises that Mr. Zygier had no connection to the Australian security services and organisations," the statement said.
It said that Israel and Australia shared "excellent cooperation, full coordination and full transparency in dealing with the issues on the agenda".
Zygier was held under alias to stem serious harm to national interests, Israel says, but has not given any other details.
In a separate measure to douse speculation of foul play, an Israeli court allowed the publication of a judge's inquiry, completed two months ago, that said Zygier hanged himself in his cell.
The investigation showed the prisoner looped a wet sheet around his neck, tied it to the bars of a bathroom window in his cell and hanged himself, choking to death.
Israeli media reported the bathroom area was not covered, for privacy reasons, by closed-circuit television cameras that transmitted images from other parts of the isolation cell.
Ruling out foul play on the basis of medical and physical evidence, Judge Dafna Blatman-Kardai said entry to the cell was monitored by cameras and examination of their footage showed no one "intervened in causing the death of the deceased".
She said his family - which has not commented publicly on the case - agreed with the findings.
"A small amount of sedative was found in his blood. There was no alcohol or drugs. This does not change my determination ... about the cause of death," a forensic medical expert was quoted as saying in the judge's report.
Civil liberties groups and some lawmakers in Israel, protesting at the state censorship restricting local reporting on the case, have demanded to know whether Zygier's rights were violated by his months of incarceration, isolated from other inmates, and whether his death could have been prevented.
Those calls were echoed in Australia, where media suggested Zygier had been suspected of betraying Mossad missions to Canberra's spy services. Australia was angered in 2010 by the fraudulent use of its passports in the assassination of a Hamas arms procurer in Dubai, which the Gulf emirate blamed on Israel.
In her report, the judge said there was prima facie evidence that the Prisons Authority had been negligent, noting that it had received special instructions on supervising the prisoner to prevent a possible suicide.
A Justice Ministry spokesman said state prosecutors would decide whether charges would be brought.
A source briefed on the affair told Reuters that Israel has since installed biometric detectors in the toilet stalls of high-risk prisoners, designed to summon guards within seconds should they stop breathing or display other signs of distress.
Responding to the media reports about Zygier, Israeli Internal Security Minister Yitzhak Aharonovitch told parliament on Monday that the detainee had received frequent family visits and been "supervised by mental-health support and treatment systems, both external and those of the Prisons Service".
Zygier also consulted with Israeli lawyers, one of whom, Avigdor Feldman, said he saw the married father of two shortly before his death to discuss "grave charges" on which he had been indicted, and the possibility of a plea bargain.
"I met with a balanced person ... who was rationally weighing his legal options," Feldman told Israeli television last week, adding Zygier had denied the charges against him.
"His interrogators told him he could expect lengthy jail time and be ostracised from his family and the Jewish community. There was no heart string they did not pull, and I suppose that ultimately brought about the tragic end."
Feldman declined to comment on an Israeli newspaper report that Zygier faced between 10-and-20 years in prison.
Deputy Prime Minister Dan Meridor on Saturday called Zygier's death a "tragedy" but said his treatment was justified.