It isn't called that way and doesn't offer the same amount of protection everywhere, but the Berne convention itself includes copyright exceptions [1] that I included in the broad “fair use” phrase.
Not the op, but it seems your linked bit of the BC justsays that countries are allowed to legislate exceptions. The only hardcoded exception is the short citation one.
[1] https://en.wikisource.org/wiki/Convention_for_the_Protection...