BAGHDAD (Reuters) - Islamic State, the al-Qaeda offshoot that seized large swathes of northern Iraq last month, has warned women in the city of Mosul to wear full-face veils or risk severe punishment.

The Sunni insurgents, who have declared a caliphate in parts of Iraq and Syria and have threatened to march on Baghdad, also listed guidelines on how veils and clothes should be worn, part of a campaign to violently impose their radical brand of Islam.

"The conditions imposed on her clothes and grooming was only to end the pretext of debauchery resulting from grooming and overdressing," said the Islamic State in a statement.

"This is not a restriction on her freedom but to prevent her from falling into humiliation and vulgarity or to be a theater for the eyes of those who are looking."

A cleric in Mosul told Reuters that Islamic State gunmen had shown up at his mosque and ordered him to read their warning on loudspeakers when worshipers gather.

"Anyone who is not committed to this duty and is motivated by glamour will be subject to accountability and severe punishment to protect society from harm and to maintain the necessities of religion and protect it from debauchery," said the Islamic State.

The insurgents, formerly called the Islamic State of Iraq and the Levant (ISIL), have been systematically stamping out any religious or cultural influences they deem non-Islamic since their lightning sweep through the north.

U.S. military and Iraqi security officials estimate the Islamic State has at least 3,000 fighters in Iraq, rising towards 20,000 when new recruits since last month's advance are included.

The Islamic State provided guidelines on how women should dress in Mosul, one of Iraq's biggest cities. The hands and feet must be covered. Wear shapeless clothes that don't hug the body. No perfume.

The insurgents run vice patrols in Mosul which answer to a morality committee which has shut Mosul's college of fine arts and physical education, knocked down statues of famous poets and banned smoking and waterpipes.

Women have been told to never walk unaccompanied by a male guardian. The Islamic State even ordered shopkeepers to cover their store mannequins with full-face veils.

A man was recently whipped in public for sexually harassing a woman.

Islamic State militants view Iraq's majority Shi'ites as infidels who deserve to be killed and have told Christians to either convert to Islam, pay a religious levy or face death.