The head of Iraq's largest church has denounced Islamic insurgents who have driven the last of Mosul's Christians out of the city, condemning their crimes as "heinous".

Reuters reports that Catholic Patriarch Louis Raphael Sako led a special church service in Baghdad on Sunday, which was attended by local Christians in addition to an estimated 200 Muslims, who came together in mutual support and solidarity following a harrowing week.

On Friday, the deadline passed for Christians in Mosul – which was captured by IS (formerly known as ISIS) militants on June 10 – to either flee the city, convert to Islam or pay a tax, jizya, for the right to continue to practise their faith.

Those who refused to comply risk being killed by "the sword".

"The heinous crime of the Islamic State was carried out not just against Christians, but against humanity," Sako declared before the congregation gathered.

"How in the 21st century could people be forced from their houses just because they are Christian, or Shi'ite or Sunni or Yazidi? Christian families have been expelled from their houses and their valuables were stolen and ...their houses and property expropriated in the name of the Islamic State.

"This has never happened in Christian or Islamic history. Even Genghis Khan or Hulagu didn't do this," he added.

Nadim Nassar, a London-based Anglican priest from Syria has denounced the international Christian community for "shamefully watching" while taking little action against persecution in the Middle East, and his words were backed up by Iraqi bishop Shlemon Wardooni.

Wardooni urged the world to "act, speak out, consider human rights," in an interview with Reuters on Sunday.

"We haven't heard from clerics from all sects or from the government. The Christians are sacrificed for Iraq," he warned.

Despite this assertion, however, Iraqi Prime Minister Nouri al-Maliki has joined the condemnation of IS, noting in a statement that militant "aggression against the churches and houses of worship in the areas under their control reveals beyond any doubt the extremist criminal and terrorist nature of this group".

Led by Abu Bakr al-Baghdadi, IS fighters – Sunni Muslims – are attempting to found a pan-Islamic state across a stretch of northern Iraq and Syria. They now control 35 per cent of Syria, as well as the Iraqi cities of Mosul, Baiji and Fallujah. It is feared that the insugents will also soon capture Baghdad.

Iraq is deeply entrenched in Christian history, and there were around 1.5 million Christians living in the country in 2003. There are now thought to be less than 200,000.