"I want all the facts made available (about the case). I want this done in days, not weeks or months," Omar told newsmen on the sidelines of a function in Srinagar.
Nazim Rashid, a 28-year-old youth, died in police custody on Sunday at Sopore in Baramulla district, a day after being detained in connection with the killing of a civilian by militants earlier in the week.
Omar said action will be taken against the persons who are guilty and an inquiry has been initiated into the circumstances leading the death of the youth.
Three policemen, including an officer have been suspended while a deputy superintendent of police has been attached pending the outcome of the inquiry. He said a murder case has already been registered in connection with the custodial killing.
Asked if any arrests have been made, Omar said, "Give us a bit of time so that nothing is done in haste that compromises the case."
The chief minister said his government was not "interested" in covering up the case or protecting anyone. "We are not interested in covering up or protecting anyone. Those responsible for the death will be an example of, so that no one dares to repeat it," he said.
On the progress made in the probe of alleged rape of a woman in Kulgam district of south Kashmir, he said the investigations have reached an advanced stage. "We have got some crucial information which will be shared with you in a day or two," he said.
A 32-year-old woman had alleged that she was abducted by two men in uniform from Manzgam area of Kulgam on July 19 and raped before being set free two days later.