Odierno attributed the long process of establishing a governing coalition to close elections.
"The political progress is slow because of the delaying of formation of the government. But I would say that's because we had legitimate, credible elections. The results were very close, and so now it's made it very difficult to form the government," he said.
Will the government be formed by the end of this month, when the U.S. plans to officially end all combat operations in Iraq?
"Our numbers of withdrawing is not linked to the [Iraqi] governmental formation process," Odierno told Amanpour.
He said he thinks "we'll see some first steps towards forming a government by 1 September, but our numbers are not linked to that formation of the government. Our numbers are linked to the capacity of the Iraqi security forces being able to sustain stability, and I think they are moving towards that capacity."
"I remind everybody that we'll have 50,000 troops on the ground post 1 September -- and that's a very significant presence to continue to assist the Iraqi security forces as we move forward," he said.
Odierno took a strong stand when asked about outside actors influencing Iraqi politics.
"I remind everyone that we still have a significant presence here. We will not allow undue malign influence on the Iraqi government as they attempt to form their government," the general said. "What we're trying to do is provide them with space and time for them to do that."
Odierno emphasized that U.S. troops were also remaining in Iraq to ensure "all the other nations respect their sovereignty as they go about forming their government."
On Saturday, an American soldier was killed in Babil province, south of Baghdad, bringing the total number of U.S. military personnel killed in Iraq since the war began in 2003 to 4,414, according to the AP.