"If they ask us that they might want us to stay longer, we certainly would consider that," Odierno told host Bob Schieffer. "That would obviously be a policy decision that would be made by the national security team and the president over time."
On Thursday, hundreds of armored vehicles in the dead of night crossed the border into Kuwait. The 4th Stryker Brigade, 2nd Infantry Division, became the last American combat brigade to leave Iraq after seven-and-a-half years. Some 50,000 American soldiers and thousands of American diplomats are still there as teachers and trainers, but it's a dramatic drawdown from the peak of more than 170,000 during the surge of American forces in 2007, which fulfills President Barack Obama's pledge to end combat operations in Iraq by Aug. 31.
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Schieffer pointed out that Iraqi Army chief Lt. Gen. Babakir Zebari told The Telegraph this week that he wants the .
Odierno said American troops' involvement in Iraq beyond that point would probably only involve assisting the Iraqis secure their airspace, borders, and other "technical" issues. The remaining 50,000 soldiers are expected to go home at the end of next year.
"That's part of us developing a long-term strategic partnership with them. That includes a security relationship,' Odierno said.
The general said Iraq forces have shown that they can handle internal security and protect Iraqis.
"They have not asked us. We'll wait to see what happens."
In other interviews broadcast Sunday, Odierno said that it would take of the Iraqi security forces for the U.S. to resume combat operations there.
"We don't see that happening," Odierno said. The Iraqi security forces have been doing "so well for so long now that we really believe we're beyond that point."
Odierno added that it may take several years before America can determine if the war was a success.
"A strong democratic Iraq will bring stability to the Middle East, and if we see Iraq that's moving toward that, two, three, five years from now, I think we can call our operations a success," he said.
Much of that may hinge on whether Iraq's political leaders can overcome ethnic divisions and work toward a more unified government, while also enabling security forces to tamp down a simmering insurgency.
Iraq's political parties have been bickering for more than five months since the March parliamentary elections failed to produce a clear winner. They have yet to reach agreements on how to share power or whether to replace embattled Shiite Prime Minister Nouri al-Maliki, and amid the political instability, other economic and governmental problems fester.
But Odierno said he is not worried that Iraq will fall back into a military dictatorship, as it was under the reign of Saddam Hussein.