Should I include the country when citing government agencies in APA?
My preference would be to just use "U.S." inline versus omission, spelling it out, or using parentheses.  Think this is adequate to give the information but is tight and doesn't look awkward.  

I would use this both in text (for example funding acknowledgements) or citations.  Also spell out agencies.  Not CIA or BUPERS but whole name. Note, it is fine in normal conversation, emails, etc. to use the acronyms if context and audience make it clear [for example in a question here about U.S. specific funding agencies I could say "NSF" in an answer].  But not in peer reviewed literature heading out to the world. 

P.s.  There is some fussiness about U.S. versus US.  I would stick with U.S. as the more traditional and common spelling. (But let copy editors do what they want--this is minutia.)  US is preferred in the context of the military and in some newer style guides.  U.S. is still more traditional in grammar texts, newspaper style guides, and civilian parts of U.S. government.