The United States said Thursday up to 900 Islamic State group jihadists have been killed in the offensive to retake Iraq's Mosul, as camps around the city filled with fleeing civilians.

Iraqis who fled their homes expressed joy at escaping IS's brutal rule as they were given shelter and assistance, in some cases reuniting with relatives they had not seen in more than two years.

The offensive, launched on October 17, is seeing tens of thousands of Iraqi fighters advancing on Mosul from the south, east and north in a bid to retake the last major Iraqi city under IS control.

Backed with air and ground support from a US-led coalition, federal forces allied with Kurdish peshmerga fighters have taken a string of towns and villages in a cautious but steady advance.

General Joseph Votel, who heads the US military's Central Command, told AFP the offensive was inflicting a heavy toll on the jihadists.

"Just in the operations over the last week and a half associated with Mosul, we estimate they've probably killed about 800-900 Islamic State fighters," Votel said in an interview.

There are between 3,500 and 5,000 IS jihadists in Mosul and up to another 2,000 in the broader area, according to US estimates.

Votel also said he had spoken with Iraqi military leaders late Tuesday who told him that as of that time, 57 members of the Iraqi security forces had been killed and another 255 or so wounded.

For the Kurdish regional peshmerga forces, numbers were lower, with about 30 killed and between 70 and 100 wounded.

- Families reunited -

The offensive has so far been concentrated in towns and villages around Mosul, with Iraqi forces later expected to breach city limits and engage the jihadists in street-to-street fighting.

Aid workers have warned of a major humanitarian crisis when fighting begins in earnest for Mosul, which is home to more than a million people, but thousands have already been fleeing surrounding areas.

The International Organisation for Migration said Thursday that 15,804 people have been displaced since the operation began, the vast majority from Nineveh province, of which Mosul is the capital.

"There's been quite a dramatic upturn in the last few days. As the Iraqi troops get closer to Mosul, more people are getting displaced, there are more populated areas," said Karl Schembri, regional media adviser for the Norwegian Refugee Council.

At a camp in Khazir, about mid-way between Mosul and the Iraqi Kurdish capital Arbil, Massud Ismail Hassan peered through a chainlink fence, looking for family members as peshmerga fighters registered the displaced.

"Once all these procedures are finished we will be able to give them food and drink and blankets we brought with us," he said.

Other families had already found each other, and tearful relatives clutched hands through the links of the fence.

Saddam Dahham, who lived under IS control in a village near Mosul for more than two years, fled to Khazir with his wife and their three children.

"We were not allowed to smoke, to use phones, not allowed to watch TV and we had to let our beards grow long," the 36-year-old said.

- Not enough room at camps -

One of the first things he did after arriving at the camp was joyfully shave the "heavy thing dangling from my chin," Dahham said.

"I'm finally going to resume a normal life," the former truck driver said.

Schembri said the Norwegian Refugee Council, other aid agencies and the United Nations were planning for 200,000 people to be displaced in the next few days, though it may not reach that figure.

If anything close to 200,000 people are displaced in the immediate future, there would be a major shortage of places in camps.

"In terms of... camp facilities, there are only spaces available for 60,000" people, Schembri said.

After seizing control of large parts of Iraq and neighbouring Syria in mid-2014, IS declared a cross-border "caliphate", imposed its harsh interpretation of Islamic law and committed widespread atrocities.

Its rule was especially harsh for religious minorities.

On Thursday two Yazidi women activists who survived a nightmare ordeal at the hands of IS won the European Parliament's prestigious Sakharov human rights prize.

Nadia Murad and Lamia Haji Bashar have become figureheads for the effort to protect the Yazidis, against whom IS pursued a brutal campaign of massacres as well as enslavement and rape.

Murad hailed the prize as a "profound message to the (IS) terrorist group that their criminal inhumanity is condemned and their victims are honoured by the free world".