"The government should immediately review cases of detenue and order the release of those not involved in heinous crimes on the eve of Eid as a goodwill gesture," MLA and state CPI-M Secretary M Y Tarigami said in a statement in Srinagar.
He said releasing 12 people was quite insignificant given the number of people who were "implicated falsely," those who have completed their prison terms and also those whose detention stands quashed by the court.
"It will be in the interest of the peace process to release innocent people from jails as a confidence building measure for the people of the state," he said.
Tarigami also condemned the alleged custodial killing of a youth in Pakharpora village of Badgam district and demanded stern action against the erring personnel.
Maqbool Ahmad Dar, a resident of Mohandpora village of Pakharpora, was arrested by the army on Friday evening and died on Saturday under mysterious circumstances.
While police said Dar died at the Nagam camp due to some medical problem he had developed during detention, people of his village staged massive protests and accused the army of killing him during interrogation.
Police and army had already ordered separate inquiries into the incident.