To fly a N- registered aircraft anywhere in the world you only need a FAA Medical Certificate. However, within Italian airspace, and because your FAA certificate is based on your Italian pilot licence, I am not entirely sure. It should be sufficient though. Again, if you fly outside of Italy you are covered.
You should get a full FAA certificate, it implies verification --possibly already done if within six months, passing a FAA written test, you already got a 3rd Class Medical, and a visit to the FSDO. Done!
Last edited by avionimc; 25th Jul 2020 at 23:13.