The Vatican is encouraging Muslim leaders to condemn the Islamic State's continued acts of terrorism in Iraq and Syria, the Pontifical Council for Interreligious Dialogue has said.

The Vatican statement said the situation for Christians, Yezidis, other religious communities and ethnic minorities in Iraq needs a clear stance from religious leaders, especially Muslim leaders.

Religious leaders are also urged to exercise their influence with the authorities to end these crimes and punish those who commit the crimes.

"All must be unanimous in condemning unequivocally these crimes and in denouncing the use of religion to justify them," the statement said.

Islamic State jihadists continue to commit criminal acts in an attempt to restore a caliphate, which had been abolished on October 29, 1923 by Kamal Ataturk of Turkey.

They have been guilty of killing people on the basis of religious orientations and have also been accused of beheading, crucifying, and hanging bodies in public places.

Aside from expelling tens of thousands of people from their homes, they have also destroyed and desecrated places of worship.

"No cause, and certainly no religion, can justify such barbarity. This constitutes an extremely serious offense to humanity and to God who is the Creator, as Pope Francis has often reminded us," the statement said.

Earlier, two leading voices in the Muslim world denounced the persecution of Christians in Iraq.

Iyad Ameen Madani, the Secretary General for the Organization of Islamic Cooperation-the group representing 57 countries and 1.4 billion Muslims said that what the IS is doing is a "crime that cannot be tolerated."

He said that the militant group's actions have nothing to do with Islam which calls for "justice, kindness, fairness, freedom of faith, and coexistence."

Turkey's top cleric, Mehmet Gormez said that "an entity that lacks legal justification has no authority to declare war against a political gathering, any country or community."

He stressed that Muslims should not be hostile towards those with different views, values and beliefs.

"The statement made against Christians is truly awful. Islamic scholars need to focus on this (because) an inability to peacefully sustain other faiths and cultures heralds the collapse of a civilization," he told Reuters news agency.