Kirkuk Police Department spokesman Amir Nuri confirmed the casualties to Anadolu.
Earlier, local authorities declared a curfew in Kirkuk amid the protests in the city, as ordered by Prime Minister Muhammed Shia al-Sudani, according to Yahya Rasool, spokesman for prime minister and commander-in-chief of Iraq.
In a written statement, he said al-Sudani ordered his security forces to launch an operation against rioters in the city and arrest them if they threaten the security.
Rasool further said only security forces are allowed to carry weapon in the city.
Al-Sudani called on political and social groups in Kirkuk to play their part in preventing potential unrest and maintaining the city's security and stability, the spokesman also said.
Supporters of the Kurdistan Democratic Party (KDP) staged a demonstration in Kirkuk on Saturday to demand the reopening of the Kirkuk-Erbil highway.
The highway was closed by Iraqi Turkmens who oppose the handover of the Joint Operations Command building to the KDP.
Protesters blocked some roads by burning tires with police firing warning shots, according to witnesses.
Ambulances were dispatched to the area, witnesses said.
Last week, protests broke out in Kirkuk against a government decision to hand over the building to the KDP, which argues that the building was previously used by them and it should be given back to the party.
Peshmerga forces of the Kurdish Regional Government (KRG) were deployed to bases evacuated by the Iraqi army in Kirkuk following the emergence of the Daesh/ISIS terrorist group in 2014.
In 2017, Iraqi government forces entered Kirkuk, ending the Peshmerga presence in the city.
Source: Anadolu Agency