Iraqi Christians are fleeing Mosul after Islamist militants threatened to kill them unless they converted to Islam or paid a "protection tax".
A statement issued by the Islamic State in Iraq and the Levant (Isis) was read out at the city's mosques.
It called on Christians to comply by midday on Saturday or face death if they did not leave the northern city.
Isis has control of large parts of Syria and Iraq and said last month it was creating an Islamic caliphate.
The ultimatum cited a historic contract known as "dhimma," under which non-Muslims in Islamic societies who refuse to convert are offered protection if they pay a fee, called a "jizya".
"We offer them three choices: Islam; the dhimma contract - involving payment of jizya; if they refuse this they will have nothing but the sword," the Isis statement said.
"Christian families are on their way to Dohuk and Irbil," in the neighbouring autonomous region of Kurdistan, Patriarch Louis Sako told the AFP news agency.
"For the first time in the history of Iraq, Mosul is now empty of Christians," he said.
The patriarch, one of the most senior Christian clerics in Iraq, said militants had been seen tagging Christian houses with the letter N for "Nassarah", a term used for Christians in the Koran.
Iraq is home to one of the world's most ancient Christian communities but its population has dwindled amid growing sectarian violence since the US-led invasion in 2003.
Prior to 2003, the number of Christians in the city had been as high as 60,000, but that had dropped to about 35,000 by June this year, Mr Sako said.
He said another 10,000 fled Mosul after Isis took control at the beginning of June and numbers dropped have fallen rapidly since.
Isis issued a similar ultimatum in the Syrian city of Raqqa in February, calling on Christians to pay about half an ounce (14g) of pure gold in exchange for their safety.