The Premier League has appealed to fans to be “positive and respectful” following recent allegations of racism and abuse in football.
Chelsea are investigating alleged racist abuse aimed at Manchester City forward Raheem Sterling last weekend.
The club has also condemned alleged anti-semitic chanting in the Europa League tie in Hungary on Thursday.
The league says while the majority of fans generate an “exciting” atmosphere, a minority have “behaved unacceptably”.
“Some brilliant football has been played this Premier League season and the vast majority of fans have generated exciting and passionate atmospheres in stadiums,” a Premier League statement said on Friday.
“However, there have been incidents recently where a very small minority have behaved unacceptably.”
“As we head into the festive season, with matches coming thick and fast, we ask all supporters to get behind their teams in passionate, positive and respectful ways.
“Support for a club should never include excessive aggression or discrimination towards the opposition.”
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Chelsea responded to offensive songs about Tottenham fans sung during the Blues’ 2-2 draw with MOL Vidi in Budapest by saying it “shamed the club”.
“Anti-Semitism and any kind of racial or religious hatred is abhorrent to this club and the overwhelming majority of our fans,” a spokesman said.
“Any individuals that can’t summon the brainpower to comprehend this simple message and are found to have shamed the club by using anti-Semitic or racist words or actions will face the strongest possible action from the club.”
Former Chelsea boss Claudio Ranieri praised his old club for being proactive.
“I think Chelsea made the right statement,” the Italian, who is now in charge at Fulham, said on Friday.
“This thing is not for football, it’s not for life. But there is a very little crowd who will say this and it’s important altogether to help make the right message to everybody.”
Everton manager Marco Silva also called for respect from fans.
“For me, you have to be all involved in this situation and to respect our opponents, to respect ourselves and to look to the football to enjoy, like a party.
“Because it is a fantastic sport, all of us love this sport and it is important to respect all of the people, not just on the pitch, around the pitch and the supporters as well.”
Meanwhile, Cardiff manager Neil Warnock wants action from government to try to tackle racism in football.
“I’d love to see the government appoint a mobile unit to go to certain games and sort them out,” Warnock said in his Friday news conference.
“Stewards aren’t really cut out to go into a pack of grown men and eject them from the ground. It needs the law to do that.”
He added: “These people are so vitriolic, and that’s gone back since I was in my 20s.”