Patriarch Sako, made the plea at an interfaith conference organised by the King Abdullah bin Abdulaziz International Centre for Interreligious Dialogue in Vienna, Austria.
He also expressed concern that Muslim leaders had not strongly spoken out against attacks carried out "in the name of the Islamic religion" which targeted Christians, Yazidis, Shi'a Muslims and others.
He said: "It is quite shocking to see the insufficiency of the official Islamic community that only denounced these acts by shy and helpless statements, showing the absence of a real role in raising the awareness of the public about the impending danger of ISIS in the name of religion."
The patriarch went on to call on Muslim scholars to refute ISIS's arguments from Islamic law and denounce their actions: "Silence doesn't befit you because ISIS and their followers will direct more distortionary strikes on Islam. "
It's dangerous to give them that chance because people will think that Islam is a threat to world peace."
Stressing that the response to ISIS had to come from within Islam, the patriarch said: "I believe, you were equally shocked as we were by the barbaric acts that swept through the towns of Mosul and the Nineveh Plain against the Christians, Yazidis and other minorities who were uprooted empty-handed from their homes and villages overnight, heading towards 'an unknown future' struck by fear and terror."
The Chaldean Patriarch went on to describe the problems faced by the 120,000 Christians who had been forced to flee their homes as ISIS advanced.
He said: "We, as minorities without protection or care, are targeted, our children are threatened and kidnapped, our homes were robbed or looted publicly as if it is legitimate (Halal)."
Adding: "Our families were living in their own homes with dignity and pride, today they live homeless in several towns and villages, in tents or in caravans or in a room which is provided rent-free from the Church."
Earlier this week the first Muslim to address the Church of England's parliament said persecution was a 'disease' that we all had to deal with.
Dr Fuad Nahdi of the group Radical Middle Way had been taking part in a panel discussion at the General Synod on the issue of religious freedom around the world.