Daesh killed 40 Iraqi troops and dumped their bodies into the Tigris River, but thousands more troops are moving into the city from the north, east and south.
The Iraqi Counter Terrorism Service (CTS) entered the state television station in Mosul, capturing the first important building in the Daesh-held city, a commander of the elite unit said.
Iraqi forces were battling Daesh on the Mosul's eastern Gogjali district earlier on Tuesday.
"Now is the beginning of the true liberation of the city of Mosul," Staff General Taleb Sheghati al-Kenani, the commander of Iraqi Counter Terrorism Service (CTS), told Iraqiya state television from Gogjali.
Iraqi forces, Kurdish Peshmerga and international coalition forces are fighting in the offensive to take back the city, which is seen as the last Daesh stronghold in the country.
Staff Lieutenant General Abdelwahab al-Saadi, a senior CTS officer, said in televised remarks that the "clearing operation is still ongoing" in Gogjali, which its forces had stormed in a two-pronged assault on Tuesday morning.
"The next (step) will be towards Al-Zahra and Al-Karama," he told AFP by telephone from the front lines, referring to two neighbourhoods on the eastern side of Mosul.
Since the offensive was launched on October 17, Iraqi troops have retaken a series of villages as they move into the city from the north, east and south.
However, the Daesh is not giving up in its fight to keep Mosul, where the group's leader Abu Bakr al-Baghdadi proclaimed the establishment of the so-called Islamic state in 2014.
Spokesperson for the UN human rights commissioner, Ravina Shamdasani, on Tuesday said Daesh had killed 40 former members of Iraqi forces near Mosul and threw their bodies into the Tigris River.
Daesh also tried to transport about 25,000 civilians from Hammam al-Alil, a town south of Mosul, on trucks and minibuses during the dead of night on Monday.
She said the group probably aims to use them as human shields to defend their positions.
Most of the trucks, which were heading towards the Tal Afar district, turned back under pressure from patrolling aircrafts, but some buses did reach Abu Saif, 15 km north of Hammam al-Alil, she added.
"We have grave concerns for these and tens of thousands of other civilians who have reportedly been forcibly relocated by ISIL (Daesh) in the past two weeks."
Daesh are taking people closer and closer to Mosul city and putting them close to their offices and to installations that could constitute military targets, Shamdasani said.
"That seems to support the assertion that they are planning to use these people as human shields, as well as ensuring that the area is heavily populated with civilians to frustrate a military operation against them."