Maulana Abdul Rauf Farooqi, leader of the political party Jamiat Ulema-e-Islam, announced at a recent press conference that he had petitioned the Supreme Court to ban the Bible.
The call is a response to the burning of a Koran by Florida pastor Terry Jones
He and others in the party claim that passages in the Holy Bible are blasphemous and offensive to Muslims.
Some of the passages that some Muslims find blasphemous relate to the story of the Last Supper, Jesus' prayer at Gethsemane, and the story of David committing adultery with Bathseba.
Farooqi's call has been condemned as "reckless" by the Centre for Legal Aid, Assistance and Settlement (CLAAS), which provides free legal support to persecuted Christians in Pakistan.
CLAAS said it was a "distortion" to claim that the contents of the Bible amountd to blasphemy, and warned that banning the Bible would criminalise Pakistani Christians.
It is "vital", the organisation said, that the Supreme Court "disregard" the legal challenge mounted by Jamiat Ulema-e-Islam.
The coordinator of CLAAS UK, Nasir Saeed, called upon the Pakistani government to take steps to reform the blasphemy laws and "deal resolutely" with attempts to harm or suppress the rights of Christians.
“At a time when Christians are being subjected to wave after wave of unprovoked attacks by Muslims, calls to ban the Bible are not only reckless but life-endangering," he said.
“Banning the Bible because it is ‘blasphemous’ would imply that anyone who even reads or owns a Bible is by default a criminal i.e. all Christians.
"This would be a deeply alarming development at a time when Pakistan should be strengthening democracy, eradicating extremist ideologies and attitudes, and building a society where all people can live as equals."
US-based persecution watchdog, International Christian Concern, said the demand by the Islamists was "additional evidence of the worsening persecution of Christians in Pakistan".
"We are concerned by this call," said Jonathan Racho, ICC's Regional Manager for South Asia.
The Rev Arif Siraji, a leader in the Presbyterian church in Pakistan, told ICC that Christians need not be worried about the call for a ban on the Bible.
"Such threats against Christianity have been happening since the inception of the faith," he said.
"Being true believers, we should encourage and pray for one another to face such circumstances, and be firm in our faith.
"We should protest peacefully, keeping in mind that our real weapon is prayer."