IRAQ'S government forces have dislodged the Islamic State group from two northern neighbourhoods in Fallujah.
An Iraqi military commander claimed the month-long offensive to recapture the city had left 2,500 IS militants dead.
The announcements came just days after the government had declared the liberation of Fallujah, the last bastion of the Islamic State group in the sprawling western Anbar province.
With aerial support from the US-led coalition, Iraqi special forces took control of the neighbourhoods of al-Shurta and al-Jughaifi, special forces' Brigadier General Haider al-Obeidi said.
He said Iraqi military engineers were clearing the streets and buildings of left-over bombs.
Teaming up with paramilitary troops and backed by the US-led coalition, Iraqi government forces launched the large-scale Fallujah operation in late May.
On Friday, Prime Minister Haider al-Abadi declared victory after special forces entered the city centre, capturing government buildings and the central hospital.
Then, Iraqi commanders said 80 per cent of the city was under their control, though clashes were still under way in its northern parts.
The counter-terrorism forces' chief in the Fallujah operation, Lieutenant General Abdul-Wahab al-Saadi, said about of 2,500 IS fighters have been killed in the offensive.
He said the number of IS fighters inside Fallujah had ranged from between 3,500 to 4,000 when the offensive began. He claimed about 15 per cent of them were foreign fighters.
He cited Iraqi police reports as saying 1,086 IS-linked suspects have been arrested. He did not say how many IS militants remain in Fallujah. Iraqi troops have not disclosed their losses in Fallujah, though the Islamic State group claims to have killed dozens
The operation has fuelled an exodus of thousands of families, overwhelming camps for the displaced run by the government and aid groups.
The UN refugee agency has said more than 85,000 people have fled Fallujah and the surrounding area since the offensive began. The UNHCR called for $17.5 million (£11.8m) to meet the immediate needs of the growing number of displaced.
UNHCR spokeswoman Ariane Rummery said she expected that thousands more "could still be planning to leave the city".
"These escalating needs have pushed UNHCR funding into crisis levels," Ms Rummery said.
"We are exhausting available resources in Iraq to deal with the rapid developments [in Fallujah]."
The extremist group still controls Iraq's second-largest city of Mosul and large parts of neighbouring Syria.
According to UN figures, the violence has forced more than 3.4 million Iraqis to flee their homes. More than 40 per cent of the displaced are from Anbar province.
