Odierno, the outgoing Army chief of staff, backed the current strategy against Islamic State, telling his last Pentagon news conference that while US troops could defeat the militants, they could not solve the broader political and economic problems besetting Iraq and Syria.
"We could probably go in there with a certain amount of American force and ... defeat ISIL. The problem is we would be right back where we are today six months later," he told reporters, using an acronym for Islamic State.
"For me it's about changing the dynamics, the political dynamics, the economic dynamics, and it has to be done by those in the region," he said.
Odierno, who has spent most of the last two decades dealing with the conflicts in Iraq, is retiring and will be succeeded on Friday by General Mark Milley, current head of US Army Forces Command.