The Pentagon convinced them to spend around two billion of their oil money to replace the AK-47 with American weapons like the M-16.
I believe the American military has become the model for the new Iraqi Army and anything they can do to copy or imitate our military adds to their confidence and professionalism. Weapons are just part of the package. I would doubt that pressure by the US alone would be enough to make the Iraqis switch from the familiar and widely accepted AK-47.