Hundreds of Christian families fled their homes in the northern city Saturday as an ultimatum threatening their community's centuries-old presence there expired.
Ban "condemns in the strongest terms the systematic persecution of minority populations in Iraq by Islamic State and associated armed groups," a UN statement said yesterday.
The United Nations chief emphasised that "any systematic attack on the civilian population, or segments of the civilian population, because of their ethnic background, religious beliefs or faith may constitute a crime against humanity."
Mosul's new rulers said there would be "nothing for them but the sword" if Christians did not abide by those conditions by 0900 GMT Saturday.
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While some families initially appeared prepared to pay the "jizya" Islamic tribute to stay in their homes, messages broadcast by mosques on Friday sparked an exodus.
Ban was "particularly disturbed by reports of threats against Christians in Mosul and other IS-controlled parts of Iraq," the UN statement said.
Before the 2003 US invasion, more than a million Christians lived in Iraq, including more than 600,000 in Baghdad and 60,000 in Mosul, as well as a substantial number in the oil city of Kirkuk and in Basra.
Until their forced exodus over the weekend, Christians had been continuously present in Mosul for about 16 centuries.