Speaking to Anadolu Agency, Maj. Mustafa Sarhank said the liberated areas include the villages of Basakhra, Bazgirtan, Tarjala and Sheikh Amir in al-Khazir front on the road connecting Mosul with Erbil.
The operation took place with support of U.S.-led coalition warplanes, he said.
“The military operations in the eastern hub of Mosul [Khazir] are taking place as per the plans of the supreme military commands,” Sarhank said.
Iraqi forces began advancing Sunday midnight on Mosul, the last Daesh stronghold in northern Iraq.
In televised statements, Iraqi Prime Minister Haider al-Abadi said only Iraqi army and police forces would be in the city.
The KRG also said a simultaneous operation has started against Daesh with the participation peshmerga forces.
Turkish-trained forces are also participating in the offensive to recapture the city, which was overrun by Daesh militants in 2014 along with vast swathes of territory in northern and western Iraq.
Recent months, however, have seen the Iraqi army, backed by a 60-nation air coalition led by the U.S., retake a large portion of that territory.