The militants, led by the Islamic State of Iraq and the Levant (ISIL) jihadist group, have begun imposing an extreme interpretation of Islamic law in the days since they took the city, residents reached by telephone told AFP.
"These militants will return us and our country hundreds of years backwards, and their laws are the opposite of the laws of human rights and international laws," said Umm Mohammed, a 35-year-old teacher.
The city, known before 2003 for its historic sites and parks and in later years as a hub for deadly violence, fell on June 10 to the militants, who subsequently overran surrounding Nineveh province and swathes of other territory.
Security forces in Mosul, a city of some two million people before the offensive, wilted in the face of the onslaught, in some cases abandoning uniforms and even vehicles in their haste to flee.
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The 16-point document announced the prohibition of the selling and consumption of alcohol and drugs as well as smoking, and forbade gatherings and carrying weapons.
Women are to wear non-revealing clothes and keep to their homes, while "shrines" are to be destroyed.
All depictions of people are considered idolatrous under the militants' extreme interpretation of Islam, and gunmen have removed various statues from the city in recent days, including some depicting famous poets.
Abu Ramzi, one of Mosul's Christians who did not flee the city, said militants destroyed a statue of the Virgin Mary in front of a church.
The militants also distributed a document to mosques in the city ordering that they not make or publish any statement not approved by ISIL, and designated a specific mosque for the acceptance of the "repentance of apostates".