The Ministry of Defense said in addition to the fatalities, nearly 100 people were wounded at the encampment near Kirkuk.
Officials said 20 Sunni gunmen were killed in the firefight and 75 others were arrested. Three soldiers died and nine others were wounded, The New York Times reported.
Tuesday's fighting in Kirkuk was the single deadliest incident in Sunni-led protests against Prime Minister Nuri al-Maliki's Shiite-dominated central government, which began in December.
Meanwhile, four people died and 13 others were injured in twin roadside bombings outside a Sunni mosque Tuesday in southern Baghdad, police said.
The incident took place as worshipers were leaving the mosque in the Dora neighborhood, CNN reported.
Sunni groups in Anbar and Salahuddin provinces began mobilizing after Tuesday's violence, declaring Jihad, or holy war, the Times reported. Armed Sunni tribesmen took control of government checkpoints in Hawija, the newspaper said.
"The peaceful demonstrations are over due to what happened today," said Saddoun al-Obaidi, a tribal leader in Hawija, a leader of the protest movement. "Now we are going to carry weapons. We have all the weapons we need and we are getting support from other provinces. This will not pass easily. Something bad will happen soon."