Iraq's Counter Terrorism Service assaulted the Al-Amil al-Oula neighborhood of west Mosul early on Friday, and were battling the terrorists inside it, said Staff Major General Maan al-Saadi, a CTS commander, AFP reported.
"The enemy fought fiercely in the first defensive line from Al-Ghazlani base to Wadi Hajar and to Al-Sumood neighborhood," Saadi said, referring to areas that Iraqi forces have recaptured since launching their assault on west Mosul on February 19.
But "after these neighborhoods, after we broke the defensive line, they lost many forces," he said.
"The enemy has begun to collapse. They have lost many of their combat capabilities. Today, the enemy sent (car bombs), but not in the numbers that they sent at the beginning of the battle."
In another sign that the terrorists are feeling the squeeze, their chief Abu Bakr al-Baghdadi was reported to have abandoned Mosul, leaving local commanders behind to oversee Daesh's defense of the city.
"He was in Mosul at some point before the offensive... He left before we isolated Mosul and Tal Afar," a town to the west, a US defense official said.
Iraqi forces launched their operation to retake Mosul in October, and recaptured the whole east bank of the Tigris river that runs through it in January.
They then set their sights on the smaller but more densely populated west side of the city.
More than 215,000 people are currently displaced as a result of the battle for Mosul, according to the International Organization for Migration. Others fled their homes but later returned.