The cancellation followed an earlier meeting with some detainees, which was prompted by reports of abuse and brutality - including the death of Akram Zuhairi - at the prison.
Zuhairi, a 42-year-old owner of a construction company and a member of the Muslim Brotherhood, died on 9 June under dubious circumstances, a Muslim Brotherhood spokesman told Aljazeera.net.
He said that fellow detainees claimed an ''accident'' left Zuhairi with a broken leg while being transferred.
As a diabetic, the injury only worsened Zuhairi's condition.
''We begged them to get x-rays taken or to see a doctor. He was clearly suffering. But they left him for eight days without any medical attention,'' Dr Muhammed Mursi, a MP, quoted the detainess as saying.
Zuhairi was a father of three.
Brotherhood rounded up
The detainees, members of the Muslim Brotherhood movement, were among the 60 rounded up in security sweeps across the country. They were charged with plotting against the state.
''This is a claim the government has used for over 70 years as an excuse to detain people,'' a Brotherhood spokesman said.
''We want this inhuman, illegal treatment of detainees to come to an end. These type of actions are unacceptable and against humanity. They have not even been examined by doctors''
Dr Muhammad Mursi,
Member of Parliament
"Many of his [Zuhairi's] colleagues have also been exposed to brutal forms of torture at the hands of the state security in Nasr City," the Committee for Prisoners of Conscience, a human rights body, said in a statement.
The Human Rights Association for the Assistance of Prisoners (HRAAP), another rights group, also voiced concern over increase in complaints of torture by state security officers.
"HRAAP expresses its concern about the continuation of the series of torture and violating the minimum legal rights for prisoners and detainees while calling on the Attorney General to open investigations into the death of Zuhairi,'' a statement said.
Dr Muhammed Mursi, other members of parliament and the NSD were allowed to visit the Turra prison on Wednesday.
They were given permission by the Attorney General to meet nine detainees from the Brotherhood. On Wednesday 9 June ''we met with four out of nine'' detainees and learnt that ''twelve, and not nine had lodged the complaint,'' Dr Mursi said to Aljazeera.net.
He said during their meeting with the detainees they were told that their time had elapsed and were asked to leave.
They were informed that further meetings would be postponed to Saturday 12 June. ''Then it was postponed again to Monday 13 June. But on Sunday all meetings with detainees were cancelled indefinitely,'' Dr Mursi said.
''Strong suspicions that the 15 deaths resulted from torture and abuse at Egyptian Police stations''
Egyptian Organisation for Human Rights
He said the MPs and members of the NSD have ''confirmed the allegations of abuse and torture by interrogators. A comprehensive report will be submitted to parliament within the next few days.''
''We want this inhuman, illegal treatment of detainees to come to an end. These type of actions are unacceptable and against humanity. They have not even been examined by doctors.''
When asked about news reports concerning doctors being allowed to visit detainees, Dr Mursi said, ''That is not true, only MPs and members of the NSD who were allowed to visit them.''
Last week, the Egyptian Organisation for Human Rights issued a report charging that at least 15 Egyptians had died while in police custody between April 2003 and 2004.
The organisation said it had ''strong suspicions that the 15 deaths resulted from torture and abuse at Egyptian police stations.''
The figure represented only a fraction of the problem, the statement said, referring to reports of hundreds of other cases of torture across the country.
A spokesman for the Egyptian Interior Ministry, which is
responsible for detentions and interrogations, said the ministry had no comment on the allegations.