Iraqi forces are so far in control of one-third of the western city of Fallujah, the Pentagon said on Tuesday, four days after Iraqi Prime Minister Haider al-Abadi declared the city liberated from the Islamic State extremist group.

"Approximately 1/3 of the city of Fallujah has been cleared by Iraqi-led ground forces," US Defence Department spokesman Matthew Allen said.

"The rest of the city remains contested and we will continue to support the Government of Iraq in eliminating ISIL from Fallujah," Allen added, saying the battle "has been and will continue to be a difficult fight."

Al-Abadi declared Fallujah, a long-standing stronghold of the Sunni extremist group some 50 kilometres west of Baghdad, to have been liberated after government forces recaptured the government compound in the city centre.

The progress by government forces in the Fallujah offensive, launched in late May, comes months after they recaptured Ramadi, the other major city in the Sunni-dominated Anbar province.

The Iraqi army declared Ramadi liberated in late December, but fighting continued for weeks in some districts.

Also on Tuesday, the US announced an additional 20 million dollars in humanitarian aid for the United Nations High Commissioner for Refugees' (UNHCR) Iraq response following its appeals for those displaced by the Fallujah conflict.

The aid is part of a larger US package coming later in the year, US State Department spokesman John Kirby said.

The UN now estimates 85,000 people have fled the fighting in Fallujah, Kirby said.

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