The fighting, near the border town of Qaim in Anbar province began after midnight and lasted several hours, said Col. Tariq Youssef, a police official in the city, 320 kilometers (200 miles) west of Baghdad.
The colonel said "a small number of the tribal fighters suffered minor wounds" and all 21 al-Qaida members in the unit were killed.
"The operation was launched by police forces backed by the Abu Faraj and Abu Shaaban tribes against members of al-Qaida," he said. "We believe that they were trying to flee the country because they are surrounded now in Anbar by the growing number of tribes that reject al-Qaida."
An increasing number of Sunni tribes in Anbar province, a stronghold of the insurgency, have joined with the government and U.S. military to expel al-Qaida from the region.