Sabah al-Norman told AFP that forces had “reached the Tigris River from the eastern (side) of the fourth bridge (the southern most bridge in Mosul)”.
The river splits the city of Mosul in two and reaching it is a key point in the battle which began on 17 October last year.
Iraqi troops have recaptured areas on the city’s east side but the western side of the city – smaller but more densely-populated – remains under IS control.
Mosul is the last Iraqi city in which Islamic State fighters hold a significant amount of territory.
Iraqi troops are expected to gain control of all of Mosul’s eastern districts before crossing the river. In any case, the bridges have all been destroyed by air strikes.
But, despite only stuttering advances in Mosul last month, the Iraqi campaign has made daily gains since resuming 10 days ago.
— Brett McGurk (@brett_mcgurk) January 8, 2017
Brett McGurk, US envoy to the coalition backing the Iraqis, said that Islamic State’s defences in the east were “showing signs of collapse”.
Heavy fighting has also been reported in the residential area of Hadba, in northern Mosul, where Iraqi forces claimed to have killed at least 50 IS fighters, according to Kurdish media.
Meanwhile, Iraqi civilians living in Mosul’s eastern districts have been trying to get their lives back to normal.
A few grocery stores have re-opened and traffic is winding through the streets, despite heavy fighting just a few miles away.
Despite many areas being without electricity, residents have started to use small generators and in some areas they are cleaning the roads and re-building.
In the southeastern district of Wahda, a hospital complex was among the buildings badly-damaged.
Iraqi soldiers said Islamic State had used parts of the building for executions and blood could be seen on one of the walls.
Most of the building, however, is burned out and parts have been mined with explosives left by the militants.