Iraqi forces have fought their way into the outskirts of the city of Tal Afar, one of so-called Islamic State’s last remaining strongholds in the country.
Counter-terrorism units entered the south-western Kifah district on Tuesday, the military said.
IS militants responded by firing rockets and deploying suicide car bombs, according to one commander.
Iraq’s prime minister launched the assault on Tal Afar on Sunday, a month after declaring victory in Mosul.
Haider al-Abadi told the estimated 2,000 jihadists holed up inside the city, along with between 10,000 and 40,000 civilians, that they should “surrender or die”.
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.