Iraqi forces have "completely surrounded" fighters with the Islamic State of Iraq and the Levant (ISIL, also known as ISIS) group in the northern city of Tal Afar, according to Iraqi and US officials.

"The enemy is completely surrounded," Ryan Dillon, spokesman for the US-led coalition against ISIL, said on Thursday in a joint press conference with Iraqi spokesman Yahya Rasool.

US-backed Iraqi forces had been making gains in their battle to retake the key area from ISIL since announcing the start of the ground offensive on Sunday.

Dillon said ISIL fighters were being deprived of their resources and at the "cusp of yet another defeat".

Rasool said around 2,000 ISIL fighters remain in the city. He added that about 300 fighters had been killed.

During his weekly press conference on Tuesday, Iraqi Prime Minister Haider al-Abadi described the progress in Tal Afar as "excellent", calling it an "indication of the enemy's collapse".

Tal Afar and the surrounding area are among the last pockets of ISIL-held territory in Iraq after victory was declared in Mosul, the country's second-largest city.

The city is located some 70km west of Mosul and about 150km east of the Syrian border, sitting along a major road that was a key ISIL supply route.

The town had a population of about 200,000 before it fell to ISIL in 2014.

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On Monday, Lise Grande, the UN humanitarian coordinator for Iraq, said that more than 30,000 people had already fled the city and surrounding areas.

"Food and water are running out, and people lack the basic necessities to survive," she said.

The Iraqi army said it believes some 10,000 civilians remain inside the city, adding that it had secured safe corridors for them.