Iraqi forces say they have broken through the defences of so-called Islamic State (IS) and reached the centre of the city of Tal Afar.
A spokesman said troops had also reached the neighbourhood around the old citadel.
Tal Afar, near the Syrian border, is one of the jihadists' last remaining strongholds in Iraq after they were driven out of the city of Mosul.
The Iraqi offensive on Tal Afar has been under way for six days.
It involves similar forces to those that finally recaptured Mosul, but also includes some units of a mainly Shia militia.
Elite units had seized the northern neighbourhoods of Nida, Taliaa, Uruba, Nasr and Saad, the Iraqi Joint Operations Command (JOC) said.
The militants remain in control of the north-eastern quarter of the city, the JOC said.
An estimated 2,000 militants are inside Tal Afar, along with between 10,000 and 40,000 civilians.
Tal Afar, which had a predominantly ethnic Turkmen population of 200,000 before it fell to IS in June 2014, sits on a major supply route between Mosul, about 55km (35 miles) to the east, and the Syrian border, 150km (90 miles) to the west.
Security sources say a disproportionate number of men from the city filled the ranks of IS as commanders, judges and members of their religious police.
The city was cut off during the nine-month Mosul offensive by troops and allied militiamen from the Shia-dominated paramilitary Popular Mobilisation (Hashd al-Shaabi) force. But they did not attempt to retake it until this week.
The UN has described conditions inside Tal Afar as "very tough", with food and water running out, and said it was preparing for thousands of civilians to attempt to escape from the city.
More than 30,000 civilians have fled the Tal Afar area since the end of April, many of them arriving at Iraqi government mustering points exhausted and dehydrated after trekking for 10 to 20 hours in extreme heat, the UN said.