He is thought to be heading north, toward Kurdish territory, and officials do not consider him a threat to leak the plan to insurgents.
Kurdish territory in modern day Iraq was granted to Iraq, under British control.
Now Kurdish territory includes a plump new swath of land.
A3 Iraq appears to be preparing to retake Kurdish territory.
The battalion initially moved north into Kurdish controlled territory to establish a security presence in the area.
The vote would allow the Pentagon to airlift troops into Kurdish territory, should it choose to do so.
In an American-led campaign, Kurdish territory would be a crucial platform for a ground assault.
Iraqi Army officials said they had recaptured about 40 mountain peaks in the Kurdish territories a few days ago.
Baghdad has made a series of gradual advances into Kurdish territory, most recently in March.
The rebels claim they strayed into Kurdish territory without permission.