The Norwegian Refugee Council (NRC) says Daesh terrorists are directly targeting civilians who attempt to flee the Iraqi city of Fallujah as government forces retake key areas in the besieged city.

"Reports from families that NRC has been in touch with describe that civilians trying to cross the Euphrates River in order to flee the fighting are being targeted by armed opposition groups," said the aid group in a statement released on Sunday.

The group, which operates refugee camps in the city, said a large number of civilians trying to cross the river have been shot and killed by the Takfiri terrorists.

In footage broadcast on state television on Wednesday, Iraqi Prime Minister Haider al-Abadi announced that the military offensive to liberate Fallujah has been slowed down due to fears for the safety of civilians being used as human shield in the city.

A truck mounted with a home-made rocket launcher is parked on the front line as Iraqi forces hold a position near the village of al-Azraqiyah, northwest of Fallujah, on June 5, 2016. (AFP)

He also said that safe corridors have been established to allow some civilians to exit.

The NRC notes that even though the majority of Fallujah's population is believed to have fled, as many as 50,000 civilians, including 20,000 children, are thought to be trapped in the city.

"Our biggest fears are now tragically confirmed with civilians being directly targeted while trying to flee to safety," said NRC country director Nasr Muflahi said."This is the worst that we feared would happen to innocent men, women, and children who have had to leave everything behind in order to save their lives."

Daesh overran Fallujah in the western Anbar province in January 2014, six months before the terror group proceeded with its offensive, taking more areas in Iraq. On May 23, the Iraqi military started a large-scale push to drive out the militants from Fallujah, located 65 kilometers (40 miles) west of the capital, Baghdad.

A member of the Iraqi government forces walks amid the rubble of a destroyed building on the front line near the village of al-Azraqiyah, northwest of the city of Fallujah, on June 5, 2016. (AFP)

Fallujah’s southern edge secured

Meanwhile, Iraqi troops have successfully retaken areas located on the edge of Fallujah.

According to Lieutenant General Abdel Wahab al-Saadi, Iraqi troops secured the mostly agricultural southern neighborhood of Naymiyah and are preparing for an offensive on the city’s main regions.

Earlier, the head of Iraq’s Popular Mobilization Units, Abu Mahdi al-Mohandis, announced that 47 villages located near the city had been liberated from the Takfiri terrorists.

Iraqi forces fire a rocket from the village of al-Azraqiyah towards Daesh positions in the city of Fallujah, on June 4, 2016. (AFP)

He added that city is now fully under siege and all the main connection routes, except for a route along the Euphrates which is used by the terrorist group to enter the city, have been blocked.

Mohandis noted that an estimated number of between 2,000 and 2,500 Takfiris currently remain in the city.

Gruesome violence has plagued the northern and western parts of Iraq ever since Daesh launched an offensive in the country in June 2014, and took control of portions of the Iraqi territory.