The Friday attack on an Iraqi police checkpoint occurred in Buhriz, a town 55km (35 miles) north of Baghdad.
The fighters first fired mortar rounds and then arrived at the scene in eight cars to open gunfire on the policemen, a police officer said, speaking on condition of anonymity out of concern for his safety.
The violence came as Shias began the three-day religious holiday of Eid al-Fitr which ends a month of fasting during the Islamic holy month of Ramadan. Most of Iraq's Sunni Arabs began to celebrate the Eid holiday on Thursday - based on their different interpretation of the lunar calendar.
In a speech marking Eid in Baghdad on Friday, a Shia leader urged voters to support his coalition in Iraq's 15 December parliamentary election.
Abd al-Aziz al-Hakim, head of the Supreme Council for the Islamic Revolution of Iraq (SCIRI), told a gathering at his party headquarters that the aim of his candidates is "to protect all Iraqis, not only Shias but also minority Sunnis and Kurds".
Two major religious parties, SCIRI and Prime Minister Ibrahim al-Jaafari's Dawa Party, form Iraq's top Shia alliance.