"After three days of fighting, Peshmerga was able to capture 120 square kilometers of territory, containing nine settlements, to the East of Mosul," Amir Sherifi told reporters.
The advance is being carried out with the support of the international coalition air cover, he added.
Some 5,000 Kurdish fighters armed by large-caliber weapons were participating in the offensive, according to Patriotic Union of Kurdistan (PUK).
The second largest Iraqi city of Mosul was captured by the militants of the Daesh, which is a militant jihadist outlawed in many countries, including Russia and the United Kingdom, in 2014. The IS overran large swathes of Syria and Iraq in 2013 and 2014.