"Islamic State of Iraq and the Levant" (ISIL) gunmen have been shooting at civilians trying to escape the month-long battle in Fallujah between the group's fighters and the Iraqi forces, local officials said.

Civilians are being attacked as they try to reach the safety of displacement camps the security forces have set up in areas to the south and west of the city, they said.

Thousands remain trapped inside the Anbar province city, officials told Mawtani, and ISIL is using them as human shields to slow the progress of the Iraqi forces.

"Terrorists have committed a massacre against families displaced from Fallujah," said Ameriyat al-Fallujah local council head Shaker al-Issawi.

"After the security forces managed to reach al-Salam intersection south of Fallujah and expel the terrorists from the area, they opened a safe corridor there to help civilians escape and reach our military units," he told Mawtani.

However, ISIL gunmen were pursuing and targeting those fleeing, he added.

ISIL shoots at fleeing families

At the beginning of the week, ISIL gunmen shot at a group of families, about 50 people traveling in total, at close range while they were trying to escape through the corridor on foot, al-Issawi said.

"The attack killed 30 people, mostly women and children from the tribes of Albu Saleh and Albu Hatem," he said, noting that the security forces returned fire and rescued the remaining civilians.

This is not the first time ISIL has targeted civilians fleeing from areas south of Fallujah, he said. Earlier this month, the group detonated improvised explosive devices (IEDs) against three escaping families, killing five people.

ISIL also has detained residents who were trying to flee and executed them in an area near the Euphrates before dumping their bodies in the river, he said.

"The killing of displaced women and children at al-Salam intersection is a despicable and cowardly act," Anbar provincial council member Athal al-Fahdawi told Mawtani.

It shows the "ugly face of those terrorists and their disregard for all human values", he said.

Shooting at fleeing civilians is "clear evidence" of ISIL's defeat as security forces continue to pound every one of the group's strongholds in Fallujah, he added.

Over the past week, security forces have liberated new parts of the city, including Subaihat, Albu Azzam, al-Nuaimiya and al-Shohada 1 and 2, he said.

The battles are now concentrated in the centre of Fallujah, he said, adding that joint army, police, tribal and counter-terrorism forces are tightening their hold on the liberated areas.

Thousands flee despite danger

ISIL has been targeting displaced families "in retaliation for the heavy losses it suffered at the hands of the liberating forces", said Lt. Col. Sabah al-Issawi, commander of the 3rd battalion of the Ameriyat al-Fallujah tribal mobilisation.

"With each progression achieved by our forces, the terrorist organisation forces families to remain in their homes under the threat of getting killed and uses them as human shields," he told Mawtani.

"Many families decide to escape the oppression of the terrorists despite all the dangers," he added.

Families usually escape during the night through safe corridors or through passages that are far from ISIL movement, he said, adding that some have been killed or wounded by ISIL's bullets and landmines while trying to flee.

"Thousands of families have been able to escape Fallujah," al-Issawi said. "They were then evacuated by the security forces to displacement camps in Ameriyat al-Fallujah, al-Khalidiya and al-Habbaniyah."

"ISIL is dying in Fallujah," he added. "It is losing dozens and hundreds of its fighters every day and its influence is waning with the liberation of most areas on the outskirts and the fighting reaching the city centre."