Elite Iraqi forces Thursday retook a town on the eastern edge of Mosul while Kurdish peshmerga opened a new front in the offensive to wrest back the jihadists' last bastion in Iraq.

Prime Minister Haider al-Abadi told an international meeting in Paris that the four-day-old offensive was "advancing faster than expected".

France and Iraq were co-chairing the meeting on the future of Mosul, which observers have warned could raise even greater humanitarian and interconfessional challenges than the massive military operation to retake it.

In some areas, the Iraqi advance was met by a trickle of civilians fleeing both the fighting and the jihadists who ruled them for two years, but the feared mass exodus from Mosul had yet to materialise.

The counter-terrorism service (CTS), Iraq's best-trained and most battle-seasoned force, retook full control of Bartalla, a town that lies less than 15 kilometres (nine miles) east of Mosul.

"I announce to the people of Bartalla and Mosul we have complete control over Bartalla," CTS commander Taleb Sheghati al-Kenani told reporters from the town.

"Its residents, its churches and all of its infrastructure are now under the control of CTS," he said of the small Christian town that IS seized when it swept across the Nineveh plain in August 2014.

Some 120,000 Iraqi Christians were forced to flee their homes at the time.

- IS drones -

Further north Kurdish peshmerga forces opened a new front with a multiple-pronged assault on the town of Bashiqa.

"The objectives are to clear a number of nearby villages and secure control of strategic areas to further restrict ISIL's movements," the peshmerga command said, using an alternative acronym for IS.

At dawn, bulldozers flattened a path for forces in armoured vehicles to carve their way down towards Bashiqa.

As tanks and personnel carriers prepared to advance, a shadow glided above them and one peshmerga shouted "drone!"

Fighters opened fire at it with every weapon available, causing an almighty din and lighting up the dim morning sky, until it fell to the ground and the troops resumed their advance.

An AFP reporter in the village of Nawaran near Bashiqa saw the downed drone, a Raven RQ-11B model similar to a booby-trapped one that killed two Kurdish fighters and wounded two French soldiers a week ago.

Iraqi federal forces and the peshmerga have not divulged casualty figures in this offensive.

On Thursday, IS released a short video showing the bodies of what it said were two peshmerga, hung by their feet from a bridge in central Mosul.

A US service member was killed Thursday when an improvised explosive device went off, the coalition said.

It said the blast occurred in northern but did not specify exactly where nor whether the service member one of the more than 100 US troops advising Iraqi forces as they push toward Mosul.

- Trickle of civilians -

To the south, Iraqi forces were making steady gains, working their way up the Tigris Valley and meeting small numbers of fleeing civilians heading the other way.

Dozens of men, women and children who escaped from the village of Mdaraj, south of Mosul, some on foot and others with vehicles, were waiting as police searched their belongings.

"We snuck out," said a man who gave his name as Abu Hussein.

The huge plumes of black smoke from fires lit by IS to provide cover from air strikes had helped them slip out unnoticed, he said.

The UN fears up to a million people still trapped inside Mosul could be forced to flee by the fighting, sparking a humanitarian emergency.

But Iraqi forces are still some distance from the city limits and no major outflows of civilians have been reported yet.

The UN's refugee agency said so far around 1,900 people had been displaced from the Qayyarah and Hammam al-Alil areas and been given assistance.

Some Mosul residents who fled before the start of the offensive have crossed into neighbouring Syria and are now sheltered at a camp in Al-Hawl.

A Kurdish official at the camp said 500 people had entered the camp in the past two weeks and 2,000-3,000 Iraqis were waiting at the border.

Bulldozers were busy expanding the camp, which staff there feared could be submerged by as many as 30,000 displaced Iraqis when the Mosul battle intensifies.

- Post-IS Mosul -

The Iraqi prime minister told the Paris meeting on Mosul that the operation to retake it was making progress.

"We are advancing faster than we had expected and planned," he said by video link.

French President Francois Hollande told the meeting that jihadists were already leaving for Raqa, their stronghold in neighbouring Syria.

"We can't afford mistakes in the pursuit of the terrorists who are already leaving Mosul for Raqa," Hollande said. "We cannot allow those who were in Mosul to evaporate."

Mosul, Iraq's second city, was seized by IS in June 2014.

Its capture touched off an offensive that saw the jihadists conquer about a third of the country and declare a "caliphate" straddling Iraq and Syria.

IS's rule has seen some of the worst war crimes in recent history and the task of reconciling all the components of the area's complex religious and ethnic mosaic is daunting.

"Given the sheer size of Mosul -- and its experience of savage rule at the hands of the Islamic State -- revenge killing will likely be an issue in the days and months ahead," according to the Soufan consultancy.

"A massive effort will be required to begin to heal what is a truly fractured city and society," it said.