i haven’t tried in a while, but i vaguely recall it’s possible using the deprecated API, but it’s still ugly to do it that way.
probably the easiest (non-automated) way to do it if you have a particular country in mind is to just get the full list of places (see https://forum.inaturalist.org/t/use-wikidata-for-place-names-and-wikipedia-descriptions/7702/13), and filter on admin_level and ancestry columns to get the places you’re interested in.
if you want to automate that process a bit, you could save off a(n abridged) version of that CSV file or put it on a server somewhere, and then you could parse through it programmatically for any country and admin level. the standard administrative places shouldn’t change often. so you typically wouldn’t need an up-to-the-minute version of the CSV file.