Forces from the Hashed al-Shaabi, a paramilitary umbrella organisation dominated by Iran-backed Shiite militias, have largely been on the sidelines since the launch of the Mosul operation.
And the western approach to Mosul, a route on which Tal Afar is located, is the only one where ground forces, which have advanced on the city from the north, east and south, are not yet deployed.
"The operation aims to cut supplies between Mosul and Raqa and tighten the siege of (IS) in Mosul and liberate Tal Afar," Hashed spokesman Ahmed al-Assadi told AFP, referring to IS's main strongholds in Iraq and Syria.
The drive toward Tal Afar could bring the fighting perilously close to the ancient city of Hatra, a UNESCO world heritage site that has already been vandalised by IS.
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Though it was not mentioned by name, the operation may also pass near the ruins of Nimrud, another archaeological site that has previously been attacked by IS.
The involvement of Shiite militias in the Mosul operation has been a source of contention, although some of the Hashed's top commanders insist they do not plan to enter the largely Sunni city.
Relations between the Hashed and the US-led coalition fighting IS are also tense, but the paramilitaries enjoy widespread support among members of Iraq's Shiite majority.
Tal Afar was a Shiite-majority town of mostly ethnic Turkmens before the Sunni extremists of IS overran it in 2014, and its recapture is a main goal of Shiite militia forces.
As the Hashed push on Tal Afar got under way, Iraq's federal police were assaulting Al-Shura, an area south of Mosul with a long history as a militant bastion that has been the target of fighting for more than a week.
The offensive operations came despite an assertion from the US-led coalition yesterday that Iraqi forces were temporarily halting their advance on Mosul for a period expected to last "a couple days.
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