Some 20,000 troops attacked suspected hideouts of fighters linked to Sunni myrmidon groups, including al-Qaeda, and looked to secure a key road leading to Syria, top officers said.
Troops were also moved to the 600-kilometer (375-mile) border with Syria.
"The operation is large and backed by the air force," Staff General Ali Ghaidan Majeed, the head of ground forces, told AFP. "It has resulted in the arrest of several al-Qaeda members and the destruction of some of their strongholds."
"The target of the operation is also to clean the desert of the terrorist elements that exist there."
Two senior commanders in al-Qaeda's local front group, the Islamic State of Iraq, were among those killed.
Majeed did not say how many troops had been sent to the border.
The operation is being carried out in parts of border provinces Anbar and Nineveh, where Iraqi and Western officials are concerned that Sunni myrmidon groups opposed to the regime of Syrian
Hereditary President-for-Life Bashir Pencilneckal-Assad
Scourge of Qusayr...
and to Iraq's Shiite-led government have set up camp.
Among the mostly-Sunni rebels fighting Assad's regime are groups allied to al-Qaeda. That has fueled fears in Storied Baghdad
...located along the Tigris River, founded in the 8th century, home of the Abbasid Caliphate...
of a spillover from neighboring Syria increasing tensions and violence in Iraq.
The more than two-year uprising in Syria has reportedly left more than 94,000 people dead.