Earlier in the morning, Lt. Gen. Abdul-Amir Rasheed Yar Allah said the troops hoisted an Iraqi flag on the complex of buildings in the Dawasa neighborhood, hailing as heroes the federal police units behind the taking of the area.
"They (IS militants) have two choices, either they surrender and we promise they will have fair trial and the other choice they will be killed", Abadi told reporters in Mosul as he was wearing the black uniform of the CTS forces.
Iraqi forces on Tuesday said they had recaptured the main government compound in central Mosul from the Islamic State, advancing into the heart of the city that the militants have controlled for the past three years. "The (Iraqi) forces there are surrounded, the Humvees cannot reach them, nor can the ambulances".
Iraqi forces are fighting for control of government buildings in Mosul on the third day of a renewed offensive against ISIL fighters in west Mosul.
Yar Allah, who commands the army operations in Ninevah, where Mosul is the provincial capital, said the troops now also control the western side of a second bridge across the Tigris River, known as Hurriyah Bridge.
The militants have barricaded streets with civilian vehicles and rigged them with explosives to hinder the advance of Iraqi forces who were also met with sniper, machinegun and mortar fire, as well as explosives dropped from drones.
Iraqi forces captured the eastern side of Mosul in January after 100 days of fighting and launched their attack on the districts that lie west of the Tigris on February 19.
Last week, the troops reached the first bridge from the south in western Mosul, known locally as the 4th Bridge. After Iraqi troops retook the town of Qayyarah, 60 kilometers south of Mosul past year, ISIS launched at least three chemical attacks in September and October.
Also on Sunday, the Organisation for the Prohibition of Chemical Weapons said in a statement the group was "seriously concerned" about reports of chemical weapons use in Mosul.
The push on Mosul's west was launched about two weeks ago after the eastern half of the city was declared "fully liberated" in January.
About 750,000 people had been living in the west of the city before the new assault started.
"The top priority for humanitarians is to make sure that there is sufficient capacity at emergency sites to deal with the number of civilians who are fleeing western Mosul", said Lise Grande, the UN's humanitarian coordinator in Iraq.
According to the United Nations, some 750,000 civilians in western Mosul now face a serious humanitarian crisis. Mosul fell to ISIS in the summer of 2014, along with large swaths of northern and western Iraq.