ICAO = International Civil Aviation Organisation
This is an umbrella organisation, that does not issue its own licences. If an "ICAO licence" is required what this means is a licence issued by a member state, whose standards reflect the Standards and Recommended Practices (SARPs) of ICAO. you would have to look somewhere pretty obscure to find a licence that is
not ICAO - certainly the common ones such as JAA, FAA, Australian CASA, Canadian, NZ, South African etc. are fine.
You should talk to the FAA, though you should also read every time I write "licence" as "license", since you yanks spell this word as a noun incorrectly