Provincial Governor Asaad Abu Gilel said a U.S. helicopter went down in the fighting near the holy Shi'ite city of Al-Najaf.
Gilel said the operation was launched after reports that insurgents planned to assassinate Shi'ite clerics and pilgrims during Ashura. Those gunmen killed were said to be both Sunnis and Shi'ites.
The Ashura festival held by Shi'a marks the death of Imam Hussein, the grandson of the Prophet Muhammad.
In Baghdad, bombings and shootings killed at least 12 people, mainly in Shi'ite areas. Among them were five girls who were killed in a mortar strike on a school in a predominantly Sunni Arab district.
Ten people were killed in a mortar attack in Jurf al-Sakhr, south of Baghdad.
And in the northern city of Kirkuk, two car bombs killed at least 11 people. Meanwhile, the U.S. military reported the deaths of thee more of its service personnel, raising U.S. losses to nearly 80 for this month.
The violence came as hundreds of thousands of pilgrims converged on the Shi'ite holy city of Karbala for Ashura.