The All India Milli Council (AIMC) said the CBI must not investigate only the alleged killers and the prison officials but should also reveal "wider conspiracy" behind the murder of Qateel Siddiui.
The AIMC also alleged that the Centre has taken "entirely untenable stand' in case of Fasih Mahmood, who is alleged to be involved in terrorist activities and presently in the custody of Saudi Arabia.
"The investigation of murder of Siddiqui must be handed over immediately to CBI. The CBI must complete investigation in a time-bound manner," Dr Mohd Manzoor Alam, Chairman of All India Milli Council, told reporters.
"There is an effort to make abnormal look normal. It seems all government offices have gone to sleep. If government cannot ensure safety of an inmate in jail, how can ordinary citizens breathe in an air of security," Ravi Nair of the South Asia Human Rights Documentation Centre said.
Terming Unlawful activities Prevention Act(UAPA) as a "black law", Alam demanded that it be repealed.
In a letter to Prime Minister Manmohan Singh earlier, Alam said, "It is an extrajudicial killing by state authority. This is how it stands: the police-intelligence personnel took him under their custody. It was their duty to ensure his protection."
The council also demanded details of the disappearance of Fasih Mahmood from Al Jubail in Saudi Arabia.