Chelsea chairman Bruce Buck has written an open letter to fans condemning the actions of “a few mindless individuals”.
Chelsea and the Metropolitan Police are investigating claims Manchester City forward Raheem Sterling was subject to racist abuse earlier this month.
The club have also condemned fans who sang an anti-Semitic chant during last week’s Europa League tie with MOL Vidi.
Buck said the actions were “unacceptable” and “unwelcome”.
“A deeply unpleasant but vocal minority which refuses to join us in the 21st century has shamed the great majority of our decent, well-behaved fans,” he added.
“Over the past weeks, months and indeed years, I have spoken at length to various Chelsea fans and supporter groups, all of whom are in full agreement that the type of behaviour we have witnessed is wholly unacceptable, hurtful and does not represent the club or the overwhelming majority of those who follow our teams home and away.”
Last week, Chelsea suspended four fans from matches while the investigation into the alleged racial abuse of Sterling takes place.
Buck greeted Blues fans at the turnstiles before Sunday’s Premier League win at Brighton, and in his letter said the club would “beat the plague that threatens to overshadow the fantastic work this club does for inclusion and equality”.
“Clearly, there remains a way to go on this journey, but we will not rest until we have eliminated all forms of discrimination from our club,” Buck said.
“We will continue to work alongside our fans, anti-discrimination organisations and football authorities to create an environment where everyone feels welcome and valued. If you do not share these values, this is not the club for you.
“We must not allow a small minority of fans to bring further embarrassment upon us, and will continue to take the strongest possible action against them.
“We are determined to win this battle, but we need the backing and action of those who share the principles of this great club.”