Here's a decent little overview of how takedown notices work in the international context.
As you'll note, it's immaterial whether a country where the infringement is occurring is a UN member state; what's important is whether that country is a member of the Berne Convention (a multilateral treaty on the protection of copyright works that is administered by WIPO).
Granted, there is a huge degree of overlap here. There are 193 UN member states, and 173 of these are parties to the Berne Convention (as are three non UN territories - the Cook Islands, the Holy See and Niue).