Iraqi government forces broke through ISIL lines inside Tal Afar on Friday and reached the old city centre and the neighbourhood around the Ottoman-era citadel, the military said.
On the sixth day of the offensive, Iraqi elite units seized the northern city's neighbourhoods of Nida' and Taliaa, the Iraqi Joint Operations Command said.
The Iraqi forces have seized about three-quarters of the city since the offensive started on Sunday, according to the latest JOC map, published on Friday evening. The militants remain in control of the north-east quarter.
Tal Afar lies along the supply route between Syria and the former ISIL stronghold of Mosul, about 80 kilometres to the east. It has produced some of the militant group's most senior commanders.
Tal Afar, which had a pre-war population of about 200,000, is the latest objective in the US-backed war on ISIL, following the recapture of Mosul after a nine-month campaign that left much of the city, the biggest in northern Iraq, in ruins.
The fall of Mosul effectively marked the end of the self-proclaimed caliphate ISIL declared over parts of Syria and Iraq in 2014. Tal Afar was cut off from the rest of ISIL-held territory in June.
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[ Pentagon chief: ISIL's days are numbered ]
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The main forces taking part in the Tal Afar offensive are the Iraqi army, air force, Federal Police, the elite US-trained Counter-Terrorism Service and some units from the predominantly Shiite Popular Mobilization Forces that began encircling the city on Sunday.
Up to 2,000 battle-hardened militants remain in Tal Afar, according to US and Iraqi military commanders. The number of civilians left in the city is between 10,000 and 20,000, according to the American military.
As in the battle for Mosul, civilians are suffering.
Waves of residents fled the city in the weeks before the battle started. Those remaining are threatened with death by the militants, who have held a tight grip there since 2014, according to aid organisations and residents who managed to flee. On Tuesday, the UN 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. People were arriving at camps for displaced people with wounds from sniper fire and mine explosions.
Two mass graves, containing about 500 bodies, have been found in Badosh, on the road between Mosul and Tal Afar, another military statement said on Friday. The dead are believed to be inmates killed by the militants when they overran a prison in the area in 2014, it said.
