The move came as Iraqi forces also captured an oil field and the main military base in the region after launching a major operation during the night, according to Iraq's Joint Operations Command.
Earlier on Monday, Iraqi and Kurdish forces exchanged artillery fire south of the city of Kirkuk, after central government forces began a "major operation" to take control of a Kurdish military base and oil fields.
Shortly before, state television announced that government troops had taken "large areas" of the province from Kurdish peshmerga fighters "without fighting", although military sources on both sides reported exchange of Katyusha rocket fire to the south of the provincial capital.
Iraqi Prime Minister Haider al-Abadi called Monday on the Peshmerga force to operate under Iraqi federal authority.
The prime minister who said this week that he was "not going... to make war on our Kurdish citizens", has "given orders to armed forces to take over security in Kirkuk," state television said.
Iraqi troops will "secure bases and government facilities in Kirkuk province" the government said. They were aiming to retake military bases and oil fields which Kurdish peshmerga fighters took in 2014 during the fightback against the Islamic State jihadist group.
Multiple peshmergas were injured in the clashes and hospitalised in Kirkuk, a local security source said.
Abadi said that members of the Hashed al-Shaabi, the paramilitary Popular Mobilisation forces, which are dominated by Iran-backed Shiite militias, would stay away from Kirkuk, where there have been multiple demonstrations against their involvement in the dispute.
"Counter terrorism units, the 9th armoured division of the army, and the federal police have recovered control of important areas of Kirkuk province without fighting," a general from the counter terrorism force said.
Two people were killed in artillery exchanges at Tuz Khurmatu, 75 kilometres from Kirkuk, which has been shaken every night since Friday by fighting between the peshmerga and Hashed al-Shaabi, a doctor at a city hospital said.
An AFP photographer saw columns of Iraqi troops heading north from the town of Taza Khurmatu, which is located south of Kirkuk.
The retaking of Kirkuk comes days after a standoff between Kurdish forces and the Iraqi army and the expiry of a deadline for Kurdish peshmerga fighters to withdraw from the areas they have controlled since 2014.
'Declaration of war'
Iraqi forces were seeking to retake the "K1 base", just eight kilometres (five miles) north of Kirkuk, which was one of the main Iraqi army bases before it was taken over by the peshmerga in 2014.
Earlier Sunday, Iraq's National Security Council said it viewed as a "declaration of war" the presence of "fighters not belonging to the regular security forces in Kirkuk", including fighters from Turkey's outlawed Kurdistan Workers' Party (PKK).
Crisis talks on Sunday made little headway in resolving an armed standoff between Kurdish and Iraqi forces in the province.
Tensions have soared between the central government and Iraqi Kurds since they overwhelmingly voted for independence in a September 25 referendum, whose results Baghdad has demanded be nullified.
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