The CII's demand to amend the laws is being presented as a way to stop people from accusing others of blasphemy without evidence.
Former Punjab Governor Salman Taseer and former Minorities Minister Shahbaz Bhatti were assassinated in 2011 for demanding the blasphemy laws be reformed to remove the option of execution and retain only the existing punishments of imprisonment and fines.
The CII announced the demand on Sept. 18 in Islamabad, Pakistan's capital, after the council decided that falsely accusing someone of blasphemy "is totally un-Islamic in nature and is also tantamount to blasphemy," the Pakistan Tribune reported.
CII member Allama Tahir Mehmood Ashrafi said the amendment would ensure "nobody dares to use religion to settle personal scores," and "will also silence critics of the blasphemy laws," Pakistan's Nation newspaper reported.
"I dedicate this effort to all those, including Salman Taseer and Shahbaz Bhatti, who have fought for righteousness," Ashrafi said after the CII announced its decision, according to the Union of Catholic Asian News.
The CII is a constitutional body that advises the legislature on whether a certain law is repugnant to Islam.
It is also tasked with ensuring compliance of state laws with principles of Islam.
Pakistan is an overwhelmingly Islamic society, and it is politically impossible to scrap the blasphemy laws or lessen its allowance of capital punishment.
The CII's recommendation was "a positive step forward," said Bhatti's elder brother, Paul Bhatti, chairman of the All Pakistan Minorities Alliance, which represents smaller religious groups and marginalized communities.
"We have been engaged in a long struggle towards this very end — to stop misuse of the blasphemy law. Hence, it is definitely a good development," Bhatti said.
APMA demanded capital punishment for false accusers in February to stop people abusing the blasphemy laws, Bhatti said.
More than 30 people accused of blasphemy have been killed by mobs during the past few decades, though no one has been executed after being found guilty in court, according to the British Broadcasting Corporation.