According to Lt. Gen. Abdul-Amir Rasheed Yar Allah, the troops hoisted an Iraqi flag on the complex of buildings in the Dawasa neighborhood earlier in the morning, hailing the federal police units who stormed the compound as heroes.
By noon, troops on the ground said the complex has not yet been fully secured and that they are battling a wave of intense ISIS counterattacks.
Sgt. Azam Ibrahim of the federal police was one of the first troops to storm the Mosul government complex. His unit then pulled back to a base on the edge of Mosul's Tayran neighborhood, saying the clashes were still underway at the complex later Tuesday.
"We were pulled back because we had killed and wounded," Ibrahim told The Associated Press. "The (Iraqi) forces there are surrounded, the Humvees cannot reach them, nor can the ambulances."
The consistent advance — more than two weeks since the new push started to clear Mosul's western side of ISIS militants — has been a major blow to the extremists who once controlled nearly a third of Iraq.
Iraqi forces declared eastern Mosul "fully liberated" in January after officially launching the operation to retake the city in October.
Yar Allah, who commands the army operations in Ninevah province, 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 the Hurriyah Bridge.
Last week, the troops reached the first bridge from the south in western Mosul, known locally as the 4th Bridge. U.S.-led airstrikes disabled all of Mosul's five bridges last year in a bid to isolate the militants.
Hours after announcing Tuesday's advance, Iraqi state TV said Prime Minster Haider al-Abadi visited the troops in Mosul. Al-Abadi was shown descending from a military plane at the city's airport and meeting with senior military officers. It was unclear if al-Abadi visited the western part of Mosul.
"They have two choices, first either they surrender and they will have fair trial and the second choice they will be killed," al-Abadi told reporters in Mosul as he was clad in a black counterterrorism forces uniform. "Some are escaping but even the escape path is closed and they have no hope, so that is why they should surrender."
He called upon Mosul residents to cooperate with the security forces, vowing to rebuild their city and to restore services.
Private broadcaster Lebanon-based Al-Mayadeen aired live footage from inside western Mosul, with thick black smoke rising from different areas as gunfire rattled. The TV footage also showed what it said were explosions from two suicide attacks carried out by ISIS militants against the security forces.
The footage also shows the city's iconic 840-year-old "Crooked Minaret," which leans somewhat like Italy's Tower of Pisa.
Unlike other heritage and archaeological sites in and around Mosul, the Islamic State militants couldn't destroy it as residents formed a human chain around it to protect it when they came to blow it up.
Meanwhile on Tuesday, the United Nations said that by Sunday, it had registered that about 42,000 people fled their homes in western Mosul since the start of the operation last month. The U.N. Office for Humanitarian Coordination, OCHA, said in a statement that 13,350 people fled to government-run areas in one day alone.
The troops expect to encounter far more fleeing civilians once they enter deeper into the more densely populated part of the city. The U.N. estimates that about 750,000 civilians are still trapped in their houses on Mosul's western side.
Mosul is Iraq's second-largest city, and its western half — the Tigris divides the city into an eastern and a western sections — is the last significant urban area held by ISIS in the country. Mosul fell to ISIS in the summer of 2014, along with large swaths of northern and western Iraq.
Salaheddin reported from Baghdad. Associated Press writer Bassam Hatoum in Baghdad contributed to this report.