FAA license is also ICAO licence. However it cannot be used to fly a aircraft registered in a JAA country commercially or vice versa.
However some countries which are not ICAO, have companies who will accept any ICAO license.
I once applied for a job in the middle east and they said it didnt matter if I used my FAA or JAA licence, both were equally accepted there.
I didnt take the job, but thats another history.