Sarabjit, 49, suffered critical head injuries in the assault by four to five prisoners with bricks and plates in Kot Lakhpat Jail in Lahore Friday.
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. His family claims he is innocent, and that he crossed over to Pakistan in August 1990 in an inebriated state, and was arrested there.
His wife Sukhbir Kaur, sister Dalbir Kaur and two daughters arrived in Lahore Sunday after grant of visa by the Pakistani government.
Sarabjit has been intubated and linked to a ventilator in the intensive care unit of Jinnah Hospital.
"Singh was diagnosed on Saturday with 3/15 glasgow coma scale (GCS); that elaborates upon his critical state of conscious level," one of the doctors treating him told Dawn.
He said the GCS was a neurological scale aimed at assessing level of consciousness after profound head injury and the reading of 3/15 indicated deep unconsciousness.
Sarabjit's treatment has thus turned out to be a major neurosurgical challenge for the medical board constituted by the authorities, the doctor said.
Anjum Habib Vohra, senior neurosurgeon and principal of the Post-Graduate Medical Institute, Zafar Chaudhry, head of Jinnah Hospital's neuro department, and Naeem Kasuri, neuro physician of King Edward Medical University are members of the medical board.
The doctor, who was not named, told Dawn that Sarabjit had suffered a critical bone fracture when he was taken to Jinnah Hospital's surgical emergency Friday evening.
During clinical assessment, it was established that Sarabjit had diffused brain injury over a widespread area of his head that led to unconsciousness.
Doctors also discovered a haematoma (a localised collection of blood outside the blood vessels) which was greater than three cm, which indicated that the patient was in dire need of surgical intervention.
However, the medical board examined Sarabjit twice Saturday and doctors were of the view that there was no need for surgical intervention at this stage.
Sarabjit is being kept in a separate intensive care unit in unprecedented police security and no one is being allowed to see him except doctors.
However, first secretary in the Indian High Commission C.S. Das paid a visit to the hospital.