"We are waiting permission for post-mortem. After that we will hand over the body of Kirpal Singh," Deputy Superintendent of Police Iqbal Shah said in Lahore.
Lahore hospital sources said the Indian High Commission was reportedly demanding that the cause of death should be given to them in writing. Only after that will the mission agree for autopsy.
The body of Kirpal Singh, 54, who according to preliminary reports died of cardiac arrest on Monday, was in the morgue of the Jinnah Hospital.
Earlier, the Indian government said it had asked its envoy in Islamabad to take up at the "highest possible level" the issue of early transportation of the body.
"Our acting high commissioner has been instructed to seek a meeting at the highest possible level in the Pakistan foreign office for early transportation of the (body)," external affairs ministry spokesman Vikas Swarup said.
"(Acting high commissioner) will also ask for official information on the cause of death," Swarup added.
Kirpal Singh died at the hospital after becoming seriously ill in Kot Lakhpat Jail.
He was alleged to have been involved in a bombing at the Faisalabad railway station in 1991 and sentenced to death for spying and terrorism in Pakistan.
Pakistani authorities said Kirpal Singh died due to heart failure.
On Tuesday, a sister of Kirpal Singh staged a protest at the Attari-Wagah checkpost on the India-Pakistan border.
"My brother was murdered just like Sarabjit earlier. The Pakistani jail authorities are responsible for his death," Jagir Kaur said.
Her reference was to Sarabjit Singh, an Indian death row convict who died in 2013 after being attacked by two Pakistani prisoners at the Kot Lakhpat Jail.
Jagir Kaur was accompanied by many others. One of them was Dalbir Kaur, the elder sister of Sarabjit Singh.
Kirpal Singh's family demanded that his body be handed over to them for cremation at his village in Punjab's Gurdaspur district.