Abdul Qadir's remarks, in an interview with The New York Times posted on the newspaper's Internet site, could become an issue in the U.S. presidential campaign.
"According to our calculations and our timelines, we think that from the first quarter of 2009 until 2012 we will be able to take full control of the internal affairs of the country," Qadir said.
"In regard to the borders, regarding protection from any external threats, our calculation appears that we are not going to be able to answer to any external threats until 2018 to 2020," he said.
President George W. Bush has said U.S. troops may have to stay in Iraq for years but most presidential candidates, especially Democrats, would like them to withdraw much faster.
Qadir is currently visiting the United States. On his agenda is weapons acquisitions for the new, U.S.-trained Iraqi army. According to the Times, these included ground vehicles, helicopters, tanks, artillery and armoured personnel carriers.
The United States disbanded the country's previous armed forces built by Saddam Hussein, the former Iraqi president who was executed in December 2006.
The United States and Iraq have said they would negotiate a formal agreement governing the legal status of American military forces in Iraq but talks have not yet formally begun.