"Christian families are on their way to Dohuk and Arbil. For the first time in the history of Iraq, Mosul is now empty of Christians," in the neighbouring autonomous region of Kurdistan, Patriarch Louis Sako said.
Witnesses said messages telling Christians to leave the city by Saturday were blared through loudspeakers from the city's mosques today.
A statement dated from last week and purportedly issued by the Islamic State jihadist group that took over the city and large swathes of Iraq during a sweeping offensive last month warned Mosul's Christians they should convert, pay a special tax, leave or face death.
The patriarch, who is one of the most senior Christian clerics in Iraq, and residents contacted by AFP said Islamic State militants had in recent days been tagging Christian houses with the letter N for "Nassarah", the term by which the Koran refers to Christians.
The statement said "there will be nothing for them but the sword if Christians reject those conditions".