Police and militia commanders had earlier said 12 militia fighters were killed in the ambush and at least 10 were missing, but security forces later found another 13 bodies dumped nearby with multiple gunshot wounds.
Islamic State claimed responsibility for the attack.
A security official said Iraqi security forces were pursuing the Islamic State militants who disguised themselves in police uniforms to carry out the attack.
Iraqi forces launched an operation this month to consolidate control of a mountain area near the oil city of Kirkuk to be used for the transit of Iraqi oil, highlighting concern about mountainous terrain where two armed groups are active.
Iraq declared victory in December over Islamic State militants who seized control of nearly a third of the country in 2014. However, the group continues to carry out attacks and bombings in Baghdad and different parts of the country.