KRG's Peshmerga forces abandoned the long-held areas a day after surrendering the city of Kirkuk.
Iraqi forces have taken control of areas previously held by Kurdish Regional Government forces in Nineveh province in northern Iraq, a military statement said on Wednesday.
The areas were evacuated by KRG Peshmerga fighters before the arrival of the Iraqi forces on Tuesday, the statement said.
The Peshmerga had taken them over the past three years as part of the war against Daesh militants.
The Mosul Dam, northwest of the city, is among the positions retaken from the Peshmerga, the military statement said.
Responding to a KRG referendum on independence held last month, Iraqi government forces backed by Iranian-trained Hashd al-Shaabi groups captured the Kurdish-held oil region of Kirkuk on Monday, transforming the country's balance of power.
Prime Minister Haider al Abadi ordered the retaking of Kirkuk on Monday, as well as all disputed areas claimed by both the semi-autonomous KRG and the central authorities in Baghdad.
Iraq asks BP for help
Iraqi Oil Minister Jabar al Luaibi has asked BP ''to quickly make plans to develop the Kirkuk oilfields,'' an oil ministry statement said on Wednesday.
BP says on its website it has provided technical assistance in the past to the Iraqi state-owned North Oil Company to aid the redevelopment of the Kirkuk field.
Kirkuk is estimated to have around 9 billion barrels of recoverable oil remaining, according to BP.