Death row prisoner, Imdad Ali, who is around 50 years old, was sentenced to death for the murder of a religious teacher in 2002.
"Imdad Ali is mentally ill and has suffered years without proper treatment," a report by local watchdog the Justice Project Pakistan (JPP) said, adding he had been diagnosed as a "paranoid schizophrenic".
15 year-old allegedly stoned to death in Hangu
JPP said it had filed an appeal against a Lahore High Court decision last month which dismissed pleas that Ali could not be executed on the basis of his mental illness.
His medical condition should be looked into, as well as the extenuating circumstances that had aggravated his mental illness during his lengthy time on death row, the organisation argued.
Ali's execution has been scheduled for September 20, it said.
Prison authorities have sent a letter - seen by AFP - to his relatives asking if they want a final meeting with him the day before his execution in the town of Vehari.
JPP executive director Sarah Belal said Pakistan would violate its international legal commitments if it executed a mentally ill person.
"Executing Imdad will exemplify Pakistan's failure to abide by its international legal commitments that forbid the death penalty for persons suffering from mental disabilities," Belal told AFP.
"Knowing what they do about his condition would make his hanging a most serious crime."
Woman stabbed to death
The Convention on the Rights of Persons with Disabilities (CPRD), which Pakistan ratified in 2011, guarantees the "inherent dignity" of individuals with disabilities, she said.
Pakistan reinstated the death penalty and established military courts after suffering its deadliest-ever extremist attack, when gunmen stormed a school in the northwest in 2014 and killed more than 150 people - mostly children.
Hangings were initially reinstated only for those convicted of terrorism, but later extended to all capital offences.
The country has executed over 400 people since resuming hangings in December 2014, according to new research by Reprieve, a British anti-death penalty campaign group.
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