UNITED NATIONS, United States - The UN Security Council has urged the international community to live up to its "moral and political obligation" to aid Iraqi civilians who fled an operation against the Islamic State group in Fallujah.

Council members on Tuesday "welcomed the successful counteroffensive" launched by Iraqi forces and coalition partners on May 22-23 to retake Fallujah, a key jihadist stronghold west of Baghdad that had been besieged for months.

IS has lost 45 per cent of the territory it held at the height of its strength, noted French Ambassador Francois Delattre, who holds the rotating council presidency.

But more than 60,000 people have been forced from their homes in the area over the past month, and a sudden influx of civilians pouring out of the city center last week has left the aid community unable to cope.

Thousands of families have nothing to eat and nowhere to sleep.

The UN’s refugee agency said 20 more camps would be needed in the coming weeks for those displaced, adding that it was "urgently" seeking US$17.5 million to meet immediate needs.

Foreign countries supporting Iraq have a "moral and political obligation" to help those in need to ensure that "those who had to flee from the fighting in Fallujah and around Fallujah will not suffer twice," Delattre told reporters.

He added that all parties involved should "respect their obligations regarding international humanitarian law."

"It is crucial that the Iraqi state makes sure that no exaction nor retaliation be committed against civilian population by paramilitary groups," Delattre said.

Prime Minister Haider al-Abadi declared victory in Fallujah last week after the national flag was raised above the main government compound. – AFP