Grande added that she has no exact information about the number of civilians who are still there.
The UN's refugee agency UNHCR said it had received some 9,000 people at the Hamman Al Alil transit centre over the past week, and it was preparing to accommodate almost 30,000 more. "Many of the displaced people from Talafar arrive exhausted and in poor health, often with critical levels of malnutrition among children, some unable to move".
Lt Gen Abdul Amir Rashid Yarallah, who is leading the Tal Afar operation, said the army had "liberated" five villages to the east of the city, while counter-terrorism forces advanced through two villages in the south west.
The city was cut off from both during the nine-month Mosul offensive by troops and allied militiamen from the Shia-dominated paramilitary Popular Mobilisation (Hashd al-Shaabi) force. They said they progressed with the help of heavy air cover.
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The umbrella organisation, which is dominated by Iran-backed Shiite militias, has already been fighting to retake other Iraqi cities from IS.
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.
USA officials, speaking on the condition of anonymity, said Mattis, who will meet Abadi and Defense Minister Arfan al-Hayali, would discuss the future of US forces in Iraq after the fall of the remaining cities under Islamic State and the role they could play in stabilizing operations.
"We prevailed in all battles against (IS), while (IS) faced death and defeat in all their battles".
"Victory is near" in Tal Afar, an "Iraqi city taken hostage and humiliated for years by attacks from these barbarians", he said.
Iraqi authorities on Monday called on ISIL militants to surrender in their last strongholds in northern and western Iraq.