The Iraqi Counter Terrorism Service has entered the building where the state television station is based in Mosul, a commander of the elite unit told Reuters.
The building's seizure is the first important milestone as forces battle for control of the Islamic State-held city.
Two weeks after Iraqi forces, backed by extensive U.S.-led ground and air support, launched their campaign to retake Mosul they have cleared several villages and towns while advancing along the Tigris river from the south.
But fighting inside the city itself, the jihadists' last big bastion in Iraq and still home to 1.5 million residents, could take months.
Iraq's special forces are encircling Mosul as fighting intensifies in areas around the edges of the city.
Forces from the Popular Mobilisation Units (PMU) are reportedly making progress despite fierce resistance by so-called Islamic State (IS) fighters who still hold the centre of the city, an Iraqi general told Associated Press.
Footage showed PMU vehicles and soldiers undertaking operations southwest of Mosul and advancing toward capturing the town of Tal Afar.
Tal Afar, a town west of Mosul, was taken over by IS in 2014.
The United Nations has received "more reports of mass killings around Mosul" by so-called Islamic State (IS) according to a spokeswoman.
Some reports suggest IS killed 40 former Iraqi security forces on Saturday and threw their bodies into a river, the UN added.
The militants also tried to "move about 25,000 civilians to Mosul from Hammam Al-Alil on Monday" but were partly stopped by US-led coalition jets.
Iraqi special forces have entered the eastern outskirts of Mosul, according to an army general quoted by the Associated Press news agency.
The troops are reportedly advancing further into the city as fighting continues.
A major offensive to retake Mosul from so-called Islamic State (IS) militants began two weeks ago.
Fierce fighting has been taking place as Iraqi troops, backed by US-led coalition airstrikes, face stiff resistance from IS militants.
Airstrikes are being used in the battle to take Mosul from so-called Islamic State (IS) fighters in Iraq, as soldiers try to breach the eastern edge of the city.
US-led coalition jets are supporting Iraqi special forces in the fight as they advance on the IS stronghold.
Iraqi troops and their allies have been bombarding IS positions on the edge of Mosul's Gogjali neighbourhood with heavy artillery, tanks and machine gun fire according to Associated Press news agency.
In the nearby village of Bazwaya, which Iraqi forces entered on Monday, smoke was seen rising from buildings where shells were landing.
Iraq's prime minister has warned so-called Islamic State to "surrender or die" as government troops close in on Mosul.Read the full story ›
The Iraqi government’s best troops made rapid progress as they pushed much closer to the eastern edge of Mosul.
Much sooner than anyone expected, two villages on the road into the city fell to the government advance and Iraqi flags were raised.
The Iraqi general in command said: “Our troops are now very close to Mosul. After liberating Bazwaia ... we are only a few hundred metres away.”
- Report by ITV News Middle East Correspondent Geraint Vincent
Iraqi elite troops appear to be edging into Mosul, following two weeks of fighting against so-called Islamic State fighters in the surrounding area.
Reuters reported an Iraqi officer as saying troops had entered the al-Karama district east of the city.
"They have entered Mosul," General Wissam Araji of the US-trained Counter Terrorism Service said.
It came shortly after a military commander said were just a few hundred metres from Mosul and could enter the city "within hours".
Shia militia groups say they are one step closer in the campaign to re-take so-called Islamic State held Mosul.Read the full story ›
The so-called Islamic State says that it has abducted nearly 8,000 families and taken them into Mosul to use as human shields.Read the full story ›