"Although it's a scant consolation, I'd like to offer a sincere apology to the family of Sanaullah and my sympathies for their loss," Omar wrote on micro-blogging site Twitter.
52-year-old Sanaullah, who was serving life sentence at Kot Balwal Jail in Jammu, was grievously injured in an attack by an inmate on Friday last. He died this morning at Post Graduate Institute of Medical Education and Research (PGIMER) in Chandigarh.
The assault came a day after the death of an Indian prisoner Sarabjit Singh who was brutally attacked by fellow inmates in a Pakistani jail.
"While the inquiry will fix responsibility for any dereliction of duty, the fact that this happened at all is a matter of great regret," Omar said.
The Chief Minister had a word of appreciation and gratitude for the medical staffof Government Medical College, Jammu and PGIMER for their efforts to save the life of the Pakistani prisoner.
"I'd also like to add a word of thanks to the doctors and staff at GMC Jammu and PGI Chandigarh for their valiant efforts to save Sanaullah," he said.