Abdul Qadir said Iraq should be able to assume internal security command by 2012, but border security would need bolstering until 2018, the New York Times reported Tuesday.
Qadir is a career armor officer who commanded Iraqi troops fighting alongside U.S. Marines in the battle for Fallujah in 2004.
Geoff Morrell, the Pentagon press secretary, told the Times Qadir's visit was laying the groundwork for a future military relationship.
"We are transitioning from crisis mode, from dealing with day-to-day battlefield decisions, to a long-term strategic relationship," he said.
President George Bush has vetoed funding bills from the Democrat-controlled Congress that attached withdrawal deadlines or quotas, and has repeatedly said U.S. troops will stand down only as Iraq's own forces grow.