Sarabjit conveyed the request when officials of the Indian High Commission met him at Kot Lakhpat jail in Lahore.
Sarabjit's daughters Swapandeep and Poonam and wife Sukhpreet Kaur are coming to Pakistan along with his sister Dalbir Kaur and her husband Baldev Singh on April 23 to meet him.
Suresh Reddy, visa counsellor with the Indian High Commission, told PTI on phone from Lahore, "Sarabjit made a very touching statement - he said he has never seen the face of his youngest daughter Poonam and would like to meet her at least once.
"When he was informed about his family members coming to Pakistan next week, Sarabjit requested the Pakistan government to be allowed to meet them."
Sarabjit, who Pakistan claims is Manjit Singh, was sentenced to death in 1991 for his alleged involvement in four bomb blasts that killed 14 people.
His family denies he is a spy as claimed by Pakistan and insists he accidentally strayed into Pakistani territory. His daughter Poonam was born after he was detained.
Sarabjit's execution was deferred for 30 days by President Pervez Musharraf last month so that Pakistan's new government could review his case following an appeal for clemency from India. He was originally to be hanged on April 1.
Presidential spokesman Maj Gen (retired) Rashid Qureshi on Saturday denied reports in the media that Sarabjit's execution had been postponed for one more month.
Sarabjit reiterated that his was a case of mistaken identity and he had not committed the crimes he was convicted for. Reddy said. "He maintained that he is Sarabjit and not Manjit. He said he had not committed any crimes and that he was wrongly condemned."
This was only the second time in nearly 20 years that Indian officials were granted consular access to Sarabjit, who was arrested in 1990.
Reddy said Sarabjit appeared to be "healthy though emotionally he was in a state of tension and stress".
India's External Affairs Minister Pranab Mukherjee on Friday made a fresh appeal to the Pakistan government to grant clemency to Sarabjit on humanitarian grounds.
There has not been any official response from Islamabad to the appeal, Reddy said.
"We have not heard anything officially but we hope that the Pakistan government will take a sympathetic view of all the appeals made regarding the staying of the execution," Reddy said.
Sarabjit had been apprised of the status of his case by other prisoners and was aware that his death sentence had been suspended for only 30 days, officials said.