Shama Bibi, who was four months pregnant, and her husband Shahbaz Masih, were killed by the group in Punjab province after it was claimed they had ripped out pages of the Koran.
Speaking to Catholic charity Aid to the Church in Need, Fr James Channan, the former Vice-Provincial of the Dominican order in Pakistan and the country's coordinator for the United Religions Initiative, said: "The UN should get involved and condemn such crimes against humanity, while appointing fact-finding commissions to investigate matters on the ground."
The couple were badly beaten before their bodies were thrown into a brick kiln and burnt.
Claims they had insulted the Islamic Holy Book were shouted from mosque loud speakers causing the mob to gather in anger.
Fr James Channan praying with members of the family of the murdered couple
Fr. Channan said he had never heard of a crime like it.
"The barbaric act by fanatic Pakistani Muslims of burning alive a poor Christian couple is a crime against humanity.
"It is the worst crime in the history of Pakistan committed in the name of religion," he said.
Pakistan's blasphemy law is often used by Muslims to settle personal disputes with people of other faiths.
Fr Channan said: "Muslims and Christians alike are victimised by controversial blasphemy laws that stipulate life imprisonment for desecrating the Qur'an and the death sentence for defaming or insulting the Prophet of Islam.
"The problem with these laws is that most often they are used to settle personal scores, such [as] business disputes.
"In any case, who in their sound mind would burn pages of the Qur'an or insult the dignity of the Prophet Mohammed?
"The Christian community is most vulnerable, since an accusation levelled against a single individual can provoke violence aimed at his or her family as well as the entire local community.
"Homes are attacked, churches are burned down and people are killed."