ISIS shoot civilians fleeing from Fallujah as the terror group tries to keep as many 'human shields' within the city 

Islamic State have shot at civilians attempting to flee Fallujah in an attempt to keep their 'human shields' in the city as Iraqi forces close in.

Families who managed to escape told of how ISIS jihadists opened fire on them as they crossed the Euphrates River on boats and makeshift rafts.

Footage carried by Iraqi channels showed civilians paddling for their lives on the river, others drifting in inflated wheel chambers. 

A displaced Iraqi woman who fled the al-Falahat village west of Fallujah holds a child as they wait to receive food and aid at the village of al-Azraqiyah, on June 4, 2016 ©Ahmad Al-Rubaye (AFP/File)

Nasr Muflahi, the Norwegian Refugee Council's Iraq director said: 'We know from witness testimonies that civilians... are being forced to stay and are being threatened.'

'People are using anything that floats, from wardrobes to plastic containers,' said Caroline Gluck, spokeswoman for the UN's Refugee Agency (UNHCR) in Iraq.

'We know that people have drowned, at least one person was shot by a sniper as he was on some kind of boat or dinghy,' she said.

In Amriyat al-Fallujah, where NRC runs the camps housing most of those who have managed to escape ISIS-held areas, there are new arrivals every day.

The battle for Fallujah: The NRC and other groups put the number of civilians trapped inside the city proper at 50,000. For them, leaving Fallujah is almost impossible

'Daesh (ISIS) shot at us when we left the city from the south. We could hear bullets zipping above our heads as we were crawling through the countryside,' said a 60-year-old woman who was too scared to give her name.

'I shouted at them that I would never go back. 'Kill me now', I said. What point is there in living if my children are suffering?,' she told AFP on the phone.

The vast majority of the approximately 18,000 people who have fled ISIS rule since Iraqi forces launched an operation to retake Fallujah two weeks ago are from outlying areas.

The NRC and other groups put the number of civilians trapped inside the city proper at 50,000. For them, leaving Fallujah is almost impossible.

'They put a car bomb on the old bridge and tell people who want to leave the city that they will blow it up against them,' said Abu Mohammed al-Dulaimi, a father of six who still lives in the city centre.

Iraqi pro-government forces and Shiite fighters from the Popular Mobilisation units fire rockets from the village of al-Azraqiyah towards Islamic State group positions in the city of Fallujah, on June 4, 2016

He said ISIS militants had sawed off the top of the car and covered it to make it less visible to enemy aircraft.

'They are under pressure... we can see it in their behaviour. I would say there is one percent of support from the population, it comes from people who get benefits from them,' he said.

- Keeping the poor -

Dulaimi said residents saw ISIS members shaving their beards Sunday for the first time, as they have done in the past to try to mingle with fleeing civilians when they are about to lose a town to the Iraqi forces.

'Daesh has been helping their own families to escape but they are trying to keep the poor people like us,' said a 25-year-old woman who reached a camp in Amriyat al-Fallujah after fleeing from Azkrakiyah, a rural area just west of Fallujah.

ISIS fighters have been moving forces along the dense maze of trails and canals flanking the river, often taking civilians with them as cover.

Displaced Iraqis who fled the al-Falahat village west of Fallujah due to fighting between Iraqi government forces and the IS group gather under a tree as smoke billows in the background at the village of al-Azraqiyah

'There's a lot of internal movement. In Garma, they forced families to move back inside Fallujah,' said the UNHCR's Gluck, referring to an area northeast of Fallujah that Iraqi forces recently liberated.

'They did the same thing in Zoba and Saqlawiya,' she said. 'We've heard this consistently from families.'

Two weeks into the offensive, elite forces are struggling to break into the city centre.

The Iraqi government has cited the risks faced by civilians used as human shields in Fallujah as the main factor slowing operations to retake the city.

But Abu Mahdi al-Mohandis, the powerful military commander of the Hashed al-Shaabi paramilitary organisation, argued the plight of trapped families was all the more reason to ramp up the offensive.

'Now Daesh is shooting at women and children to prevent them from leaving,' he told reporters on Sunday.

'It's clear that this city is hostage to these gangs, we are not going to just stand here with our hands tied.'

Shiite fighters from the Popular Mobilisation units hold an IS flag in the village of al-Azraqiyah, Fallujah