The clashes came as Sunni and Shia political groups jockeyed for position ahead of the December 15 general elections by pooling their respective forces into election alliances.
Militiamen from the Mehdi Army had asked police for backup in recovering a comrade who was being held in Al-Khazaliyah, but the combined group was hit by insurgents as it prepared to launch the operation, an interior ministry source said.
The other two dead were policemen, while 12 militiamen were wounded.
The troubling upsurge in inter-communal tensions came after US ambassador Zalmay Khalilzad said political progress could allow the United States to withdraw some of its troops next year.
"I do believe it's possible that we could adjust our forces, downsizing them in the course of next year," the US ambassador told media in Washington.