BAGHDAD — Military operations in Iraq this past week were one-sided, with Iraqi government forces using superior numbers and firepower to reclaim disputed areas that had been controlled by separatist Iraqi Kurds since 2014.

But in the public relations war, the two American allies are vying on a more level battlefield to win international support and sympathy just days after Iraq drove Kurdish fighters from almost all of the contested areas.

The Kurds and Baghdad traded accusations after a battle on Friday in which Iraqi government forces reclaimed the last Kurdish-held area in oil-rich Kirkuk Province.

The two sides blamed each another for firing the first shots, and for using weapons supplied by the American-led coalition that were intended for use against Islamic State militants. Kurdish fighters known as pesh merga ultimately withdrew from the town of Altun Kupri and retreated into the Kurdish autonomous region, Iraq’s military said.