General Peter Schoomaker said "the power of information" and how the conflict is portrayed and perceived also has a major impact on the outcome.
"This war that we're in cannot be won militarily," he told defense reporters here.
He said US forces are doing better than media coverage would suggest and they are gaining valuable experience in fighting the kind of asymmetrical adversaries that the United States is likely to face in the future.
But he noted that national power consists of the diplomatic, informational, military and economic.
"Military -- the "m" in the dime -- will not win this," he said. "This will be won at the informational level and at the economic level, with the support of the military for security, and diplomatically."
"This is a tug between whether or not nation states, rule of law, civilization are going to succeed over everything that is the reverse of that. It really is a clash of ideas," he said.
"And this notion of how people are informed, what they think, and how it's described is a very powerful piece of this deal," he said.
"So are we winning? Well, we're not going to win it militarily. We are going to win it when Iraqis take ownership," he said.
How they do that "will not be exactly consistent with Jeffersonian democracy," he said.
But he said it offers "an extraordinary opportunity to have a different Middle East."