A second secret prisoner is being held in same jail that Israeli-Australian spy known as Prisoner X killed himself in 2010

Israel is holding a second unidentified security prisoner in conditions of extreme secrecy, according to court documents released this week in relation to Prisoner X, the Australian-Israeli secret agent who hanged himself in jail in 2010 and whose case caused a sensation when it was exposed earlier this year.

The existence of another top-secret prisoner was acknowledged in the Israeli parliament on Wednesday, although no details were disclosed.

But former foreign minister Avigdor Lieberman described it as "an exceptionally grave case", and the lawyer for Ben Zygier, who was dubbed Prisoner X when details of his case were revealed in February, said the second prisoner's alleged offences were "sensational".

Israel insisted it was acting within the law in regard to secret prisoners held in isolation and whose identity is concealed even from prison guards.

The existence of "Prisoner X2" was revealed in an appendix to a document released by the justice ministry on the circumstances of Zygier's death. It referred to "a separate prisoner jailed in Block 13", a high-security cell in Ayalon prison. No further details were contained in the document.

Lieberman, the chairman of the foreign affairs and defence committee of the Israeli parliament, told politicians: "Following all the talk about prisoners X, Y and Z, I want to emphasise that the state of Israel abides by the law and all these incidents are being closely supervised by the legal and parliamentary establishment … Israel protects all the rights of prisoners in accordance with the law. We handle the matter scrupulously, even though this is an exceptionally grave case."

The public security minister, Yitzhak Aharonovitch, denied that he had lied when he said in the aftermath of disclosures about Zygier that there were no other secret prisoners in Israeli jails.

On Wednesday he told parliament: "There are indeed no disappeared prisoners in Israel whose families don't know of their arrest. Nor are there disappeared prisoners whose cases aren't handled by the legal authorities."

He added: "Nevertheless, sometimes there are cases whose existence cannot be widely publicised, in order to prevent damage to national security. In these cases a judicial gag order is imposed.

"There are also sometimes cases in which it is necessary to hold a prisoner under a false name to prevent damage to national security. But even in these cases all the prisoner's rights are meticulously protected, and these prisoners are certainly not 'concealed' from the courts."

Avigdor Feldman, who was Zygier's lawyer, confirmed the existence of a second secret prisoner at the time his client was being held in isolation. Speaking on an Israeli radio station, he said "Prisoner X2" was male, an Israeli citizen, Jewish, and worked for the secret services.

Asked to compare Prisoner X2's alleged offences with Zygier's, Feldman said: "Without getting into details? Much more grave. Much more sensational. Much more amazing. Much more riveting."

The reasons for Zygier's detention are still unknown. The Australian Broadcasting Corporation, which revealed his identity in February, later said he had unwittingly sabotaged a secret operation to return the bodies of Israeli soldiers missing in Lebanon back to Israel. The Mossad, the Israeli secret service body for whom Zygier was an agent, was forced to abort the operation.

Zygier, an Australian Jew from Melbourne, had moved to Israel to join the Mossad around 10 years before his death. He was secretly imprisoned by the Israeli authorities for a number of months before hanging himself in his cell in December 2010. The outcome of disciplinary proceedings against six prison guards and officers in relation to Zygier's suicide is expected soon.

Zygier's family is reported to be seeking compensation over his death, saying the Mossad and the prison service were aware he was a suicide risk. According to the court documents released this week, Zygier's mother emailed one of his lawyers from Australia on the day of his death, saying she feared he could be suicidal following a rift with his wife.

Prisoner X2 is being held in the same high-security facility. According to a report in Thursday's print edition of Haaretz, based on accounts from prison service officials, Prisoner X2 is held in a cell without windows, has no contact with other prisoners or jailers, and prison guards do not know his identity or any charges on which he has been convicted.

He is allowed a short, solitary walk in a courtyard each day, and is monitored by security cameras around the clock.