"Kurdish peshmerga, with US air support, have seized control of the eastern side of the dam" complex, Major General Abdelrahman Korini told AFP.
"We killed several members of Daash. We are still advancing and in the coming hours should announce welcome news," he said, using the old Arabic acronym for the Islamic State jihadist group.
Witnesses said the air strikes started early in the morning and reported that fighting was ongoing in the afternoon.
Peshmerga forces lost control of the dam on August 7 as IS fighters were sweeping the region, conquering one village after another and seizing other key infrastructure such as oil wells.
The dam on the Tigris river, on the southern shores of Mosul lake about 50 kilometres north of the city, provides electricity to much of the region and is crucial to irrigation in vast farming areas in Nineveh province.
A 2007 letter to the premier, Nuri al-Maliki, sent by then US ambassador Ryan Crocker and the former commander of US forces in Iraq, David Petraeus, warned of the consequences of a disaster at the dam, which was assessed to have serious structural weaknesses.
"A catastrophic failure of Mosul dam would result in flooding along the Tigris river all the way to Baghdad," the letter read.
"Assuming a worst case scenario, an instantaneous failure of Mosul dam filled to its maximum operating level could result in a flood wave 20 metres deep at the city of Mosul," it said.
The Islamic State has already resorted to the weaponisation of dams, as was the case earlier this year when it flooded large areas around the city of Fallujah, west of Baghdad.
However Mosul is the main stronghold of the Iraqi part of the Islamic State's self-proclaimed "caliphate", and the dam would be an important part of its own economy and state-building efforts.