The twin attack which happened on Sunday, in the al-Rashad region south of Kirkuk city, took place just after midnight, Al Jazeera’s Mahmoud Abdelwahed, reporting from the capital Baghdad, said.
The attackers first engaged in a military confrontation with police officers that lasted about two hours, killing three officers.
Reinforcements coming to the area were killed in an ambush using explosives planted on the roadside, Abdelwahed said.
Three police officers were also wounded in the attack and another was missing.
There was no immediate claim of responsibility but ISIL fighters are active in the area and a security source said the group was involved.
Separately, at least three Iraqi soldiers were killed and one was wounded on Sunday when gunmen attacked an army checkpoint southeast of the Iraqi city of Mosul, security sources said.
ISIL seized swaths of Iraq in a lightning offensive in 2014, before being beaten back by a campaign supported by a US-led military coalition.
The Iraqi government declared the group defeated in late 2017, but it still has sleeper cells that continue to hit security forces with asymmetric attacks.
The cells regularly target the Iraqi army and police in the north of the country, but this attack was one of the deadliest this year.
A July 19 bombing claimed by ISIL officially killed 30 people in al-Woheilat Market in Sadr City, a Shia suburb of Baghdad.
International coalition troops in Iraq currently number approximately 3,500, of which 2,500 are US troops.
However, Washington has been drawing down its military presence amid attacks on facilities it uses by Iran-aligned armed groups and has said that, from next year, the role of US troops will be limited to training and advising their Iraqi counterparts