There have been fierce clashes between Kurdish and Iraqi troops north of Kirkuk city, days after the Iraqi army took control of disputed areas.
A BBC correspondent at the scene said there had been rocket, artillery and machine-gun fire in Alton Kupri.
The district is the last area in Kirkuk province still held by Kurdish Peshmerga fighters.
Iraqi forces have this week taken over swathes of territory which had been held by the Kurds since 2014.
Army and allied militia launched an operation which saw Kurdish forces pushed back into the officially recognised autonomous Kurdistan Region of Iraq (KRI).
The oil-rich province of Kirkuk, which includes ethnically mixed Kirkuk city, is claimed by both the central government in Baghdad and the KRI.
Iraqi Prime Minister Haider al-Abadi ordered military action after the Kurdish government held a referendum which overwhelmingly backed independence. Mr Abadi had declared the vote illegitimate.
An Iraqi military spokesman said counter-terrorism and federal police forces, as well as Iranian-backed militia, advanced on Alton Kupri at 07:30 (04:30 GMT).
The BBC’s Richard Galpin, who was at a checkpoint in the area, said there was a “major outbreak of fighting” with large numbers of military vehicles and soldiers heading to the scene.
The Iraqi army’s media department, the War Media Cell, said it had taken control of Alton Kupri (known as Perde in Kurdish), though this has not been confirmed.
The area lies on the northern edge of Kirkuk province, about 30 miles (50 km) south of the Kurdish capital, Irbil.
The latest action comes a day after an Iraqi court ordered the arrest of Kurdistan’s vice-president for calling troops sent to Kirkuk this week “occupying forces”.
Peshmerga forces had controlled much of the province since 2014, when Islamic State (IS) militants swept across northern Iraq and the army collapsed.