"The military units' withdrawal (from Al-Qaim, Rawa and Ana) was for the purpose of redeployment," Lieutenant General Qassem Atta said, referring to it as a "tactical" move.
Witnesses said insurgents moved into Rawa and Ana, in Anbar province, yesterday evening, after security officers and witnesses also reported militants entering Al-Qaim earlier in the day.
Anti-government fighters have held all of one city in Anbar and areas of a second since early January.
Beginning late on June 9, militants led by the Islamic State of Iraq and the Levant (ISIL) but also including a number of other groups such as loyalists of executed dictator Saddam Hussein, overran most of one province and parts of three others north of Baghdad.
The security forces wilted in the face of the initial onslaught, in many cases abandoning vehicles, equipment and even their uniforms.
They appear to have recovered in the past few days, with officials touting gains against militants, though insurgents have made territorial progress elsewhere.
The United States has offered up to 300 military advisers to help Iraq stem the tide, but has stopped short of acceding to Baghdad's request for air strikes, calling instead for more inclusive leadership by the Shiite-led government.
The crisis has alarmed the international community, with the United Nations warning that it was "life-threatening for Iraq".