The assailants in the town of Balad, 80 km (50 miles) north of Baghdad, sprayed machine gun fire from their cars for around 10 minutes before speeding off.
Hours later a suicide bomber set off his explosive vest at a nearby vegetable market after police and militia members cornered him in a disused building and exchanged gunfire, security sources said. Four were killed and two critically wounded, medical sources added.
There was no immediate claim of responsibility for the attacks but the area, which was nearly overrun by Daesh (ISIL) militants in 2014, remains around 40 km from a frontline held by militiamen.
The attackers had passed three police checkpoints before reaching their target, said police sources who declined to be identified as they were not authorized to speak to the media.
Security forces deployed throughout the town Friday morning, fearing more attacks, Reuters reported.
Iraqi authorities have come under heightened criticism over security breaches that allowed suicide attackers to set off three bombs Wednesday in Baghdad, killing at least 80 people in the bloodiest day in the capital so far this year.
The country is also facing a political crisis over a cabinet overhaul that has crippled government for weeks and threatens to undermine the war against Daesh, which still controls swathes of territory in the north and west which it seized in 2014.
One of the shooting victims, a 22-year-old named Tahseen, told a doctor at Balad Hospital he had been smoking a water pipe when a man wearing civilian clothes and a bandolier filled with ammunition crossed the street towards the cafe. He described several blasts, likely from stun bombs, amid the shooting.