The plea for mercy for Aftab Bahadur Masih, who is due to be hanged tomorrow, comes after another prisoner condemned to death in contentious circumstances was granted a last-minute reprieve.
According to the Justice Project Pakistan (JPP), a human rights law firm handling his case, Masih was only 15 when he was arrested over a murder in the eastern city of Lahore.
The JPP say he was convicted on the basis of a confession extracted through torture from his co-accused Ghulam Mustafa, along with another eyewitness, and both have since retracted their statements.
"The execution of this innocent man, arrested as a child, should immediately be halted," Reprieve's Maya Foa said in a statement.
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Church leaders also appealed for a reprieve for Masih, who is a Christian.
The Roman Catholic Bishop of Karachi, Joseph Coutts, has written to President Mamnoon Hussain asking for Masih's hanging to be delayed so his case can be investigated.
In a separate letter several other church leaders including Michael Nazir-Ali, the former Bishop of Rochester in Britain, also called for clemency.
"To execute Mr Bahadur in these circumstances would be to commit a grave injustice."
Some two dozen activists and relatives of Masih held a protest outside Lahore Press Club demanding that the execution be stopped.
"Give justice to Aftab, Stop his execution," the protesters shouted.
Masih's brother, Babar Bahadur, told AFP that his sibling was implicated in a "false case and police tortured him to obtain a confession."