The AMS is an international organization. It appears to deal with zombie-related infestations, as shown in The House of the Dead: Overkill and after the Curien incident. Its true purpose is never stated, however, but it appears to be outside of other US Government organizations and/or jurisdiction (for example, when G confronts Papa Caesar, he specifically places him under "AMS Arrest", though this may just be an example of the purposely bad writing).
By 2019, following a world-wide outbreak of zombies, it is obvious AMS is no more. However, former agent Thomas Rogan forms a paramilitary group to combat the undead threat that roams the world.
The Zombie Revenge instruction manual claims that the AMS is an American agency, though this information is likely not considered canon.