The Counter-Terrorism Service (CTS) had taken control of the eastern bank of the Tigris river, which bisects the city from north to south, Lieutenant General Talib Shaghati told reporters in Mosul.
Army units are fighting Daesh in a collection of northeastern districts the militants remain holed up in, the military says.
The army, special forces and elite police units have operated in tandem to capture different areas of eastern Mosul.
The army is mostly deployed in the north, the Counter-Terrorism Service (CTS) - which has spearheaded advances - in the east, and the federal police in the south.