The body of 52-year-old Sanaullah was handed over to officials of the Pakistan Embassy after completion of the post-mortem by a Medical Board at the PGIMER hospital and various formalities by local authorities, including police.
A special PIA plane had arrived here from Pakistan to take the body back, an official spokesman told PTI here.
The media was not allowed inside the air terminal when the body was being taken into the aircraft.
"Sanaullah was declared dead around 7 am today. He had multiple organ failure due to severe head injury. The team of doctors headed by Prof Y K Batra tried their best to revive him," a Medical Bulletin issued by Post Graduate Institute of Education and Medical Research(PGIMER) said.
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He was injured in a scuffle with an Indian inmate in the high security Kot Balwal jail in Jammu on Friday and rushed to the PGIMER hin an air ambulance.
Sanuallah was serving a life term after he was convicted under TADA provisions following his arrest in 1999.
Pakistan demanded that India should conduct "a fair and impartial inquiry" into the prisoner's death.
"We will also demand from the Government of India to immediately release 47 prisoners of Pakistan who have already completed their sentences," the Commission Press Attache said.
An official spokesperson in the Ministry of External Affairs earlier said India will facilitate Pakistan's request to repatriate the body of Sanaullah and will provide necessary assistance.
A Pakistani response to the proposal is awaited, the spokesperson said.