Iraqi and Kurdish forces Wednesday pushed further towards Mosul, Islamic State's de facto Iraqi capital, on the third day of a mission to recapture the city, even as they encountered surprise resistance in some surrounding towns and villages.

Iraqi forces were advancing quicker than expected, a top US general supporting the operations said, and there were indications that some Islamic State leaders and fighters were leaving Mosul.

"The Iraqis are ahead of where I thought they would be when this operation started," said General Gary Volesky, the commander of US land forces in operations against Islamic State.

"There are fewer ... Daesh [Islamic State] fighters today than there were yesterday and there'll be fewer tomorrow than there are today."

Islamic State is likely to "give up terrain until they can get into the complex urban areas of Mosul because that's where they can offset some of the technological advantages we have," Volesky said.

An Iraqi military official, who asked not to be quoted by name, said that troops were advancing towards Mosul from three directions on the eastern front and had captured the village of Kani Haram.

Around the village of Abbas Rajab, the official said, fierce fighting was taking place as troops advanced. Iraqi forces had taken the village the previous day but had been forced to leave when Islamic State militants attacked them from hidden tunnels, he said.

The official said there was heavy fighting too around the town of Qaraqoush, some 15 kilometres south-east of Mosul, which Iraqi forces had entered the previous day without apparent resistance, only to be surprised by jihadists concealed in nearby tunnels.

Islamic State has previously used tunnels and booby-traps to hamper the advance of Iraqi and Syrian forces on its strongholds and carry out surprise attacks behind their lines.

On the southern front, meanwhile, police general Shakir Joudat said police troops had captured the village of Arfila some 60 kilometres south of Mosul and were advancing northwards.

Volesky said that initial operations had gone "pretty well."

There had been no sign so far of major refugee movements, he added: "In fact, a lot of the villages, as the Iraqi security forces have come in, have helped the Iraqis."

Islamic State captured Mosul and other large areas of Sunni-populated northern and western Iraq in a lightning offensive in mid-2014. After a series of gains by security forces over the past 18 months, it is now the only major Iraqi city held by the jihadists.

French Defence Minister Jean-Yves Le Drian Wednesday said that the battle for Mosul would be long, but that France was committed to supporting the offensive.

He told the lower house of parliament in Paris that as the Iraqi capital of Islamic State, Mosul was the strategic centre where terrorist attacks that hit France have been conceived and organized.

"We have to target the centre and eliminate the centre in order to be able to focus on what has metastasized," he said.

Meanwhile, the International Committee of the Red Cross said its staff was assisting in the screening of civilians fleeing Mosul to government-held territory and ensuring humane conditions for anyone who was detained.

Iraqi Prime Minister Haider al-Abadi has promised safe passages for civilians. Earlier this year, people fleeing the Sunni city of Fallujah as government forces moved in said they had witnessed killings and other abuses by pro-government Shiite militias.

“One of the areas where ICRC, together with the Shia militias and the Iraqi government, has focused most in the past couple of months is the screening procedures after attacks," ICRC President Peter Maurer said during a visit to the Ethiopian capital Addis Ababa.

The role of the Shiite militias in the battle for Sunni-populated Mosul has been controversial, and al-Abadi has said they will not enter the city itself.

On Tuesday a prominent militia leader, Abu Mahdi al-Muhandis, said the militias would fight on the western approaches to Mosul and liberate the town of Tel Afar some 65 kilometres to the west, which has a partly Shiite population.

The UN Refugee Agency (UNHCR) said in a statement that its working with its to finalize preparations to provide emergency assistance for families displaced by the anticipated intensification of the conflict in Mosul in Iraq.

It said that over 912 refugees have crossed from Baaj in Ninewa governorate into Syria and reached a camp for internally displaced at Al Hol in al-Hassakeh in northeast Syria. 

"Reception capacity is being reinforced at Al Hol in order to be ready to accommodate displaced Iraqis.  In the initial phase, arrangements are made for 15,000. This capacity will be increased to 30,000 with the final target of 50,000," the statement said.

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