Lieutenant-General Abdul Ameer Rasheed Yarallah said Counter Terrorism Service forces spearheading the seven-week operation to retake Mosul seized the Tamim district halfway between the city's eastern edge and the River Tigris running through its center.
The elite troops, part of a US-backed, 100,000-strong coalition of Iraqi forces, have been fighting street battles with the militants and now control around half of the city's eastern neighborhoods.
But progress has been slow as they have faced counterattacks by the jihadist fighters, who deployed hundreds of the suicide car bombs, as well as mortars and snipers, and used the city's million residents as human shields.
Yarallah also said in a statement that air strikes by Iraqi F-16 jets destroyed three production plants making car bombs in Mosul and three weapons stores. He gave no further details.
Iraq launched the operation to recapture Mosul on Oct. 17. Defeating Islamic State in the largest city under its control would deal a major blow to its self-styled caliphate in Iraq and Syria, and its ambitions to govern territory.
In Iraq, it has already been forced to retreat from Tikrit, Ramadi and Falluja, although its ultra-hardline Sunni Muslim fighters still hold large parts of remote, Sunni regions near the Syrian border, and an area of land southeast of Mosul.
December 9 push in eastern Mosul follows advances by Iraqi troops three days ago in the southeast, when soldiers surged into the city and briefly seized a hospital which was also believed to be used as a base by the militants.
The swift attack marked a change in tactics after weeks of slow-moving, fighting where soldiers have painstakingly sought to clear neighborhoods block by block. But the rapid gains also left the soldiers vulnerable to counterattack.
The army pulled out of the hospital under heavy fire and called in an air strike on militants inside the complex. After more than 48 hours of fierce back-and-forth fighting, tanks from an armored division were stationed in the Wahda neighborhood where the hospital is located, residents told Reuters by phone.
A video released on December 9 by Islamic State's Amaq news agency gave an indication of the brutality of the fighting around the Salam hospital. Outside its gates, a tank or armored vehicle was still burning in the middle of a cratered street.
Inside a hospital building, windows were blown out and ceiling panels collapsed. Armed men showed off weapons, ammunition and rocket launchers that they described as the "spoils" of combat, as well as the corpses of dead men in uniform.
One fighter promised to cut the heads off Shi'ites - referring to the Iraqi troops - and stamp on their bodies. "Nineveh state will be your graveyard," he said, referring to the north Iraqi province where Mosul is located.
Outside the hospital building a collection of blackened military vehicles, so heavily damaged that a tank's turret and tracks had been blown clean off, were bunched together.