Iraqi forces drive towards Kurdish peshmerga positions on October 15, 2017, on the southern outskirts of Kirkuk.

Iraqi army units have seized positions in and around Kirkuk, a major oil city that's dominated by the country's Kurdish people, who voted for independence last month.

Iraq's U.S.-trained Counter Terrorism Service has taken control of the provincial government headquarters in Kirkuk, and the Iraqi flag is flying over disputed areas, Reuters reported. The Iraqi national army also took over the North Oil Company, a refinery in Kirkuk, oil fields and an air base, according to news agencies.

Reports indicated that the Iraqi troops had not faced significant opposition from Kurdish peshmerga militia fighters in the area. However, the General Command of the Peshmerga Forces responded strongly to the advance, local news reported.

"The attack is a clear declaration of war against the people of the Kurdistan Region," the General Command said in a statement.

The Iraqi units went on the move toward Kirkuk around midnight local time in order to "safeguard" the area, military commanders said.

An aid group said several peshmerga fighters and Iraqi soldiers had been killed in a clash south of Kirkuk overnight, according to Reuters. There were no other reports of fatalities.

The U.S. Central Command, which coordinates the campaign against Islamic State militants in Iraq and Syria, said it was aware of gunfire exchanges overnight. The engagement appeared to be a misunderstanding that occurred in the dark of night, it said on its website.