"I think that they continue to grow. We continue to see development in planning, and in their ability to conduct operations.
"The Iraqi people are resilient. They want this. They want to have a democratic country. They want to be on their own. They want to be moving forward and be a contributor to stability in the Middle East."
Despite the advances in building up Iraq's security apparatus, Odierno conceded there were scenarios where the US military might have to resume combat operations.
"If, for example, you had a complete failure of the (Iraqi) security forces. If you had some political divisions within the political forces that caused them to fracture, but we don't see that happening," he said.
"They have been doing so well for so long now that we really believe that we are beyond that point."
But massive security challenges remain, and the extent of the country's political problems was highlighted this week when the winner of the general election five months ago broke off coalition talks with his main rival.
Thursday's pullout, a major step in the handing back of power to the Iraqi people, came two days after a suicide bomber killed at least 59 people at a Baghdad army recruiting centre in Iraq's deadliest attack this year.
Pullout 'on schedule'
Earlier this month, the country's top military officer warned that American forces may be needed for a further decade.
"If I were asked about the withdrawal, I would say to politicians: the US army must stay until the Iraqi army is fully ready in 2020," Lieutenant General Babaker Zerbari told AFP news agency.
Barack Obama, the US president, will make a major speech on Iraq next week.
Obama, who was an opponent of the Iraq war from the beginning and made a campaign promise to withdraw US forces as quickly as possible, has insisted the ongoing pullout is on schedule and will not be altered
Under a bilateral security pact all US forces must leave Iraq by the end of 2011, but Odierno said special training units could remain, noting similar security arrangements with Saudi Arabia and Egypt.
"Potentially we could be there beyond 2011," he said.
"If the government of Iraq requests fielding systems that could help them with external threats."