The former detainees said they were pressured, under the use of painful techniques, to admit to crimes they had not committed.
"Our hands [were] tied and eyes covered so we couldn't see the torturers. The informants were dictating to them that 'This guy did this, or did that'. And he was swearing to God that this guy has performed that action," one of the men said.
"But we were all innocent."
The man showed dozens of cigarette burns that he said were inflicted on him by prison officers with the full knowledge of authorities.
He was one of hundreds of men rounded up by security forces in October as part of a crackdown on Sunni fighters in northern Iraq.
They were held at al-Muthanna until the human rights ministry gained access to the prison and closed the facility.
"We were tortured for four long months continuously," another former detainee said.
"Whether you recognise or not, whatever they want you to say, they keep torturing you and the prisoners. They died in the torture."
The local council of tribes for the Nineveh province, where most of the former detainees were from, held a protest on Wednesday calling for the government to respect the rule of law.
|The Iraqi human rights ministry insists there are no secret prisons in the country
Fares Abdallah al-Fares, the leader of the Nineveh tribes' council, said: "Torture goes against human dignity. What is a man without his dignity?
"We ask the prime minister and minister of defence to apologise to the people of Nineveh."
In a recent report, the Los Angeles Timesclaimed that facilities such as al-Muthanna are "secret jails" run by elite forces that answer only to Nouri al-Maliki, the prime minister, and stand outside the normal rule of law.
Wijdan Salim, the Iraqi human rights minister, dismissed the existence of "secret" facilities at a news conference in Baghdad, and said the government would be sueing the Los Angeles Times for the false claims.
Salim did however acknowledged that numerous abuses had been reported at the Baghdad prison, and said they were being investigated.
Earlier in the week, Kamil Amin, a spokesman for the human rights ministry, confirmed to Al Jazeera that serious legal violations had been committed at al-Muthanna prison.
"Our teams have received complaints that the prisoners are not getting enough legal consultation and suffer from very slow procedures that take much longer than they should," Amin said.
However, he refused to answer questions about whether there was any evidence of torture of the inmates at the facility.
The UK-based human rights group Amnesty International has urged Iraqi authorities to investigate the allegations of abuses.
Source: Al Jazeera