He says the popular target groups rally is expelled from the city of Tal Afar, cutting off supply routes jihadist to Mosul from Syria.
Tal Afar was a majority Shi'ites swept by him in 2014. The city of Mosul, a Sunni, Shiite militias and is committed to not enter.
Iraq's offensive began last week.
Iraqi and Kurdish forces advanced and the coalition backed by the US Air Force in pressure to regain control of Mosul, is in fact the capital of Iraq.
He added that the operation was launched from the area south of Mosul.
During previous military campaigns against it, Shiite militias have been accused of committing serious crimes, including war crimes against civilians year.
It is believed that up to 1.5 million people stay in Mosul.
There are fears that the use of human shields also closed the operation in the city.
The United Nations said Friday it is that militants kidnapped tens of thousands of civilians from areas around the city to be used as human shields.
He added that the United Nations and the jihadist group as about 190 former members died in the Iraqi security forces and 42 civilians, apparently for refusing to obey orders.