Led by Sarabjit's sister Dalbir Kaur, his wife Sukhpreet Kaur and daughters Swapandeep and Poonam crossed the Attari-Wagah joint check post on their way to Lahore, some 20 km from the international border between India and Pakistan.
The family offered prayers at Harmandir Sahib, the holiest of Sikh shrines in Amritsar, popularly known as Golden Temple, Sunday morning before leaving for the border, 30 km from Amritsar.
"We are going there with lots of hopes. We want to bring him back hale and hearty. His condition is such that there is some fear in our hearts. We have offered prayers to the almighty to help him recover fast," Dalbir Kaur said before leaving for Pakistan.
She said the family has been granted visas for 15 days to visit Pakistan. Authorities there have allowed one member of the family to be with Sarabjit in hospital.
The Pakistan High Commission in New Delhi issued the visas to the family Saturday evening as a special case after doctors in Lahore's Jinnah Hospital hospital described Sarabjit's condition as "critical" and "in deep coma".
"We did not want to go to Pakistan in these circumstances. We are praying that he (Sarabjit) recovers fast. We want to bring him back to India for treatment," Sarabjit's daughter Swapandeep said.
"We are hoping that he will recover and we will not have to get our visas extended," Swapandeep said.
She demanded that Sarabjit be shifted to a better facility. "We are very concerned about his condition. The authorities should immediately shift him to a good hospital with better facilities. This (Jinnah) hospital does not have adequate facilities," Swapandeep said.
Sarabjit, 49, suffered critical head injuries in an unprovoked and sudden assault by four to five prisoners with bricks and plates in Lahore's Kot Lakhpat prison Friday evening.
He has been on death row in Pakistan since 1990 after being convicted by Pakistani courts for bomb blasts in Lahore and Multan, which left 14 people dead.
Sarabjit's family claims he is innocent, and that he crossed over to Pakistan in August 1990 in an inebriated state, and was arrested there.
Police in Pakistan, however, claim that Sarabjit Singh, known as Manjit Singh, was involved in terrorist strikes.