Iraqi forces battled to retake the Assyrian Christian villages of Tel Asqof and Batnaya north of Mosul on Saturday.
The neighbouring Iraqi villages were seized by Islamic State in August 2014, prompting the residents to flee.
Meanwhile, the Iraqi army also launched an operation on Saturday to take Qaraqosh, a Christian town about 20 km (13 miles) southeast of Mosul, which was also emptied of its population in 2014.
Iraqi special units earlier this week captured Bartella, a Christian village north of Qaraqosh.
The offensive that started on Monday to capture Mosul is backed by the U.S.-led coalition. It is expected to become the biggest battle fought in Iraq since the U.S.-led invasion in 2003.
The army is also trying to advance on Mosul from the south while Kurdish Peshmerga fighters are holding fronts in the east and north of the city.