Pakistan hanged three convicted murderers on Wednesday, the same day Amnesty International criticised it for becoming the world's third most prolific executioner after China and Iran.

Chaudhry Arshad Saeed Arain, a senior prisons official, said the executed men were brothers Muhammad Imran and Muhammad Luqman, convicted over the murder of a man in Islamabad in 1996; and Raheel Ahmed, who gunned down a man in 1994.

Pakistan unveiled a sweeping plan to curb militancy after Taliban attackers gunned down more than 150 people, most of them children, at an army-run school in Peshawar in December 2014.

A six-year moratorium on the death penalty was lifted and the constitution amended to allow military courts to try those accused of carrying out attacks.

The number of known executions worldwide rose more than 50% last year to at least 1,634, the highest figure recorded since 1989, Amnesty International said in a report on Wednesday - with the surge largely fuelled by Iran, Pakistan and Saudi Arabia.

"Over the past year, Pakistan has vaulted to the number three spot for recorded state executions in the world - a shameful position no one should aspire to," Champa Patel, director of Amnesty's South Asia office, told AFP.

Pakistan executed 326 people last year, Patel said.

"Most of those executed were not convicted of terror-related offences, and there is evidence that at least two and possibly more of them were juveniles when they committed their alleged crimes."

The overwhelming majority of those hanged since the government fully restored the death penalty in March 2015 had no links to terrorism, said Sarah Belal, director of the Justice Project Pakistan which advocates the abolition of hanging and represents death row convicts.

She said weaknesses in the judicial system and a lack of fair trials raised the possibility that many sent to the gallows were innocent, underage at the time of their crimes or mentally ill.