Liverpool and Manchester City say they are "fully committed to dealing with unacceptable behaviours" following trouble at their recent games.
The clubs and their fan groups held a meeting in November after which they all committed to improving relations.
The two sides have sent a joint letter to supporters asking them to report any incidents "that cause harm".
The move comes before they meet at Etihad Stadium in the Carabao Cup fourth round on Thursday.
"The passion and enthusiasm that we see from our fans when we play each other - at the Etihad Stadium or Anfield - is part of what makes matches between our clubs so special," said the letter from Liverpool chief executive Billy Hogan and City counterpart Ferran Soriano.