"Around more than a third of the right bank (west Mosul) is under the control of our units," Staff Major General Maan al-Saadi told AFP.
Mosul is split by the Tigris River, and its eastern side is referred to as the left bank, while the western is known as the right back.
Iraqi forces launched the operation to retake west Mosul - the most populated urban area still under ISIS control - on February 19, pushing up from the south.
ISIS overran large areas north and west of Baghdad in 2014, but Iraqi forces backed by US-led air strikes and other support have since retaken most of the territory they lost.
Iraqi forces launched a major operation to retake Mosul in October, recapturing the eastern side of the city before setting their sights on the smaller but more densely-populated west.