The claim comes only hours after a spokesman for the UN's High Commissioner for Human Rights, Navi Pillay, said she was 'extremely concerned' about reports of 17 executions in Iraq's second largest city.
The church leader who can't be named for security reasons spoke to Premier's Des Busteed on the News Hour.
The US Secretary of State says he's 'laser-focused' on resolving the crisis in Iraq.
The Islamic State of Iraq and Syria (ISIS) militants have taken over towns and cities across the country as part of a bid to create a new Islamic state in the region.
John Kerry has called for unity, he said: ""Political division, fuelled by ethnic or sectarian differences simply cannot be allowed to steal from the Iraqi people what so many have given so much for over the course of these last years."
America's refusing to send troops to Iraq, but the US President says there are other options to be considered.
Meanwhile the Iraqi government's sent troops to the outskirts of Baghdad in case militants try to overrun the capital.
Further fighting has broken out between Sunni and Shia militia, as concerns grow of a civil war which could tear the country apart.
General Lord Richard Dannatt, who's a Christian, used to head up the British Army and thinks this is solely about religion.
He said: "This is a bitter fight within the Muslim world itself and you've got fanatical people being encouraged to be taken on by what'll probably be by Shiite militias.
"And we know from our own experiences in Basra some years ago how dangerous and effective they can be."
It comes as Iraq's most senior Shia cleric has told people to take up arms against hard-line Sunni insurgents seizing control of towns across the country.
Half a million refugees are now thought to be fleeing the violence.
Meanwhile, oil prices have reached a nine-month high in the wake of events in Iraq.
The country's the second-biggest producer in the so-called OPEC cartel.
The price of Brent crude now stands at just under 67-pounds.