The Lahore High Court directed the Vehari District and Sessions Judge to probe the incident and submit a detailed report within a week.
"A judicial inquiry will thoroughly probe the matter and fix the responsibility," the LHC office said.
Last month, police arrested Ghulam Mustafa, 30, and Liaquat Ali, 28, from Ghagoo Mandi in Vehari district of Punjab, some 340 kilometres from Lahore, in connection with cellphone and electric wire theft.
During interrogation, the police officials allegedly cut off the left hands of the accused.
Khuda Bakhsh, father of Mustafa, said police subjected his son and the other accused to severe torture in the custody after they failed to get a bribe.
"The policemen responsible for the gruesome act should be given exemplary punishment," he demanded.
Islamic laws suggest the punishment of chopping off the hands of a person for committing theft.
The police official accused in the incident, however, had claimed the accused had attempted to commit suicide by cutting off their left wrists.
Station House Officer Aslam Cheema said both the suspects had cut their wrists with blades in a bid to "commit suicide".
Although Sadiq Ali Dogar, district police officer Vehari, suspended five police officers, including Cheema, and registered a case against them, the police have managed to get a statement from the accused, saying they cut off their left hands to commit suicide.
Doctors at the hospital, where both the accused are being treated, say it was not possible for the accused to cut off their left hands on their own.
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