Does he have the authority to do this?
No he doesn’t. The CMP does not “tightly control the importation of obsolete military weapons”. The CMP gets all of its firearms from the Army.
Many countries were armed after WWII under the Military Assistance Program (MAP) where they were LOANED firearms to rearm their military. Over the years as those countries declared the firearms obsolete, they were simply returned to the ARMY. Since the Army also considered them obsolete, they turned them over to the CMP.
Other countries like South Korea bought the firearms outright and now have a large surplus (up to 1 million rifles and carbines) that importers have bought and have been trying for years to get permission to import but have been blocked by both the Bush and Obama administrations.