Kurdish forces launched a major assault on Thursday on a town held by the Islamic State group near Mosul, opening a new front in the offensive to wrest back the jihadists' last Iraqi bastion.
Prime Minister Haider al-Abadi told an international meeting in Paris that the offensive was "advancing faster than expected" as it entered its fourth day.
France and Iraq were co-chairing the meeting on the future of Mosul, which observers have warned could raise even greater 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 has yet to materialise.
The main target of the latest Kurdish push was the town of Bashiqa, northeast of Mosul.
Iraqi forces also pressed assaults towards the city from the east and south.
Outside Bashiqa, Kurdish peshmerga forces backed by US-led coalition air strikes advanced in armoured vehicles and brought down two small drones IS was using for reconnaissance purposes.
The peshmerga command issued a statement saying the "large-scale operation" was launched at 6:00 am (0300 GMT) near Bashiqa, northeast of Mosul.
"The objectives are to clear a number of nearby villages and secure control of strategic areas to further restrict ISIL's movements," it said, using an alternative acronym for IS.
An AFP reporter in Nawaran, outside Bashiqa, saw one of the two drones neutralised by the peshmerga, a Raven RQ-11B model similar to a booby-trapped unmanned aircraft that killed two Kurdish fighters and wounded two French soldiers a week ago.
"These drones belong to IS... So we shot this drone and brought it down. As you can see, the peshmerga destroyed it," said General Aziz Weysi, commander of the peshmerga's elite Zaravani task force.
"These drones can do observation and can explode. They sent this one but it did not explode," he told AFP.
Iranian Kurdish rebels of the Kurdistan Freedom Party (PAK) were involved in the operation alongside the peshmerga and apparently taking a frontline role.
East of Mosul, where the peshmerga launched the offensive on Monday, Iraq's elite federal counter-terrorism service was taking control of Bartalla, a town whose mostly Christian residents fled the IS advance two years ago.
"We started breaching Bartalla early today. There are only 750 metres (yards) to cover to reach the centre," Lieutenant General Abdelwahab al-Saadi, who is commanding operations in the area, told AFP by telephone.
"There is resistance, we already blew up three car bombs today," he said.
Bartalla, which lies less than 15 kilometres (10 miles) from the eastern edge of Mosul, saw fierce resistance from the jihadists earlier this week.
Iraqi forces were also poised to attack nearby Qaraqosh, which was the largest Christian town in Iraq before IS swept across the Nineveh plain in August 2014, forcing everyone to flee.
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.
He said that the huge plumes of black smoke from fires lit by IS to provide cover from air strikes had helped them slip out unnoticed.
"We raised white flags and went towards them," Abu Hussein said, describing how they approached Iraqi security forces.
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.
"Reports indicate that military activities remain concentrated in less populated areas, with no large-scale civilian displacement recorded at this stage," UN aid chief Stephen O'Brien said late Wednesday.
The Iraqi prime minister told the Paris meeting on Mosul's future 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."
Iraq's second city was seized by IS in June 2014.
It 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," the Soufan consultancy said in a recent brief.
"A massive effort will be required to begin to heal what is a truly fractured city and society," it said.