A supporters' trust in Leicester is calling on fans to work together to avoid hooliganism.
Ian Bason, chairman of the Foxes Trust - a Leicester City's supporters group - said recent violence was "appalling".
Arrests were made during the past two matches involving Leicester City - first at home against Norwich City and last weekend at Coventry.
Leicestershire Police said the two clashes were not linked, and they were expecting to make more arrests.
Eleven people were detained and later released after the fights in Coventry and 13 men were arrested after the Norwich City match.
Mr Bason said: "I don't think, if you are the fan of a football club, you should do anything to detract from the reputation of the club. I don't think these people should even be called fans."
He added: "They are using [the games] to have an excuse for a punch-up."
Coventry City FC said in a statement that the violence had "nothing to do with the club" and pointed out it took place "more than five miles from the Ricoh Arena".
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