Sami al-Aridhi, a lieutenant general in the Counter-Terrorism Service, said his men had retaken a military base and a village southwest of Mosul and entered a residential neighborhood of the city.
"We have attacked and fully control Ghazlani base, we have also taken Tal al-Rayyan... and we're attacking Al-Maamun neighborhood," he told AFP.
Iraqi forces secured the east side of Mosul a month ago and Sunday launched a fresh push on the west side of the Tigris River that divides the city.
They have since retaken several outlying villages and desert areas near the city.
On Friday, commanders confirmed that government forces had full control of the airport that lies on the southern edge of the city.