Iraqi forces and pro-government paramilitary units said Friday their sights are on the jihadist-held citadel in the centre of Tal Afar after recapturing several districts from the Islamist State group.

"The Iraqi flag has been hoisted in Al-Nasr district," an eastern neighbourhood of the city, the Joint Operations Centre said in a statement.

"The troops are now at the entrance to the district of the citadel," which dates back to the period of Ottoman rule, the JOC said.

It said Counter-Terrorism Service special forces had also retaken Al-Taliaa district to the south and were tasked with expelling IS from the citadel, the last current target of the CTS in Tal Afar.

On the sixth day of an offensive to recapture the city launched between the CTS, Shiite fighters of the Hashed al-Shaabi and the federal police force, police have seized the Saad district and were moving into Al-Qadissiyah, the JOC said.

After routing the jihadists from Iraq's second city Mosul in July following a gruelling nine-month-long battle, Iraqi forces launched an assault Sunday on Tal Afar, where an estimated 1,000 jihadists are holed up.

The attackers have faced an onslaught of suicide and car bomb assaults.

The International Organization for Migration said "thousands of civilians" had fled Tal Afar since the offensive began.

But around 30,000 civilians are trapped by the fighting, according to the United Nations.