Italy expects FIFA to announce a punishment Friday.
De Rossi elbowed U.S. forward Brian McBride in the face in Saturday's 1-1 draw, earning a red card and drawing blood from a cut under McBride's left eye. The cut required three stitches to close.
In the letter, De Rossi took full responsibility for his error and explained how he apologized personally to McBride after the game. De Rossi also apologized for damaging soccer's image.
FIFA will also consider Uruguayan referee Jorge Larrionda's report on the incident and TV replays.
The red card automatically prevents De Rossi from playing in the final group game Thursday against the Czech Republic.
Coach Marcello Lippi has indicated that Italy is also expecting a multigame ban.