About three quarters of Tal Afar remains under militant control including the Ottoman-era citadel at its centre, according to an operational map published by the Iraqi military.
Lt. Gen. Abdul Amir Rashid Yarallah, commander of the "We are Coming Tal Afar" offensive, announced the Federal Police and Shiite Hashd al-Shaabi liberated the neighborhoods of Qadisiya1, Qadisiya2, and Rabiaa in northwestern Tal Afar Saturday morning.
Last month, Iraq declared victory over IS in Mosul, the country's second largest city, after a grueling nine-month campaign. Tal Afar is located roughly 60 kilometers east of the Iraq-Syria border.
Since Mosul fell to government troops, Tal Afar is the last IS enclave in the province.
As the effort to retake Tal Afar got underway, the US-led coalition estimated that between 10,000 and 50,000 civilians remained in and around the city.
Several villages north of Tal Afar have yet to be retaken, the statement said. On Tuesday, the United Nations refugee agency said those who had fled were suffering from dehydration and exhaustion, having lived off unclean water and bread for three to four months.
The jihadist group has lost much of the territory it controlled and thousands of its fighters have been killed.
"God willing, the remaining part will be liberated soon", Iraqi Foreign Minister Ibrahim al-Jaafari said earlier at a news conference with his French counterpart, Jean-Yves Le Drian, and French Defence Minister Florence Parly, in Baghdad.