The Islamic State group has threatened Christians in the Iraqi city of Mosul with death if they do not convert to Islam or pay a tax, Al Jazeera has learned.

The Sunni rebel group issued the orders in a letter after Friday prayers. The document, obtained by Al Jazeera, states that the order was issued after Christian leaders failed to attend a meeting called by the group.

In response, the group says in the letter that Christians must either convert to Islam, pay a tax on non-Muslims known as jiziya, or give up their posessions and leave the city. Failure to do so would result in a death penalty, "as a last resort".

Mosul, Iraq's second largest city, was overrun by the Islamic State group and allied rebel groups last month.

The Iraqi army units stationed in the city, most of whom were Shia, fled after the group crossed from Syria and attacked the north of Iraq.

Before the attack, Mosul's Christian community was estimated at 3,000. Many are believed to have already fled the city as part of an exodus of up to one-third of the population. Those who fled reported that churches and Christian-owned shops in the city were smashed.

The Islamic State's leader, Abu Bakr al-Baghdadi, held a sermon in Mosul's grand mosque two weeks ago, calling on all Muslims to unite behind his group.

The Islamic State, formerly known as ISIL, has issued similar demands in areas it control in Syria, and has posted pictures of Christians being crucified for disobeying orders in Raqqa.

Church leader‎s in Iraq have not responded to the threats officially.

Nickolay Mladenov, the head of the UN assistance mission In Iraq, condemned the order.

"Any persecution of minorities constitutes a crime against humanity and we urge all sides to protect civilians. We have produced a report listing attacks on civilians ‎and have brought this up at the highest levels of the Iraqi government."