Zulfiqar Ali, 52, was transferred Monday to Nusakambangan prison island off Java where executions take place, and Indonesian authorities have told Pakistani officials his execution is imminent.
Rights groups including Amnesty International have expressed serious concerns about Ali's conviction, alleging it arose out of beatings and torture and he did not have a fair trial.
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Maryam Haq, legal director at the Justice Project Pakistan (JPP), said: "He was tortured relentlessly and deprived of his most basic legal rights.
"Given that there is stronger evidence to support his innocence than guilt, it is now time for the President of Pakistan to appeal to our Muslim allies and save an innocent Pakistani's life."
Pakistan's deputy ambassador in Jakarta, Syed Zahid Raza, said earlier on Monday his embassy has "approached all the concerned high officials to convince them that it was not a fair trial".
Rights groups have claimed Ali, sentenced to death in 2005 for heroin possession, was beaten into confessing.
Amnesty said Ali, a father of six, was arrested at his home in West Java province on November 21, 2004, and charged with possession of 300 grams of heroin.
He was not allowed access to a lawyer until about one month after his arrest, the group said in a statement in May.
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It added that while Ali was being interrogated by police, he was kept in a house for three days and punched, kicked and threatened with death unless he signed a self-incriminating statement, which he later did.
He was hospitalised and required stomach and kidney surgery after the beatings, the statement continued.
"During his trial he described this torture, but the judges allowed the 'confession' to be admitted as evidence. There has been no independent investigation into his allegations," Amnesty added.
Indonesia executed 14 drug convicts, mostly foreigners, in two batches last year.
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