Some 20,000 troops attacked suspected hideouts of fighters linked to militant 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 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.
The operation is being carried out in parts of border provinces Anbar and Nineveh, where Iraqi officials are concerned that militant groups supporting the terrorists in Syria set up camp.
Among the militants fighting against the Syrian government are groups allied to Al-Qaeda. That has fuelled fears in Baghdad of a spillover from neighboring Syria increasing tensions and violence in Iraq.
Syria has been struggling with a western-backed insurgency which began in March 2011 as a protesting movement soon turned to be a cover for terrorist groups including al-Qaeda and al-Nusra Front.
The United States, Israel, UK and their allies as well as several Arab countries, including Qatar and Saudi Arabia have been supporting the armed insurgency in Syria, mulling ways to supply the militants with more arms to topple the legitimate government of Syrian President Bashar al-Assad.