Chelsea have suspended four people from attending matches while an investigation into the alleged racial abuse of Manchester City forward Raheem Sterling takes place.
The incident involving the 24-year-old occurred during City's 2-0 loss at Stamford Bridge on Saturday.
Chelsea are "fully supporting" an ongoing police investigation.
A club statement said evidence of racist behaviour will result in "severe sanctions, including bans".
"Chelsea Football Club finds all forms of discriminatory behaviour abhorrent," the statement continued, adding that the club "will also fully support any criminal prosecutions".
- Press coverage 'emboldens racist rhetoric'
- Bournemouth's Mings pulls out of Talksport interview over Sterling coverage
- Reality check: Is football racism rising?
- Invisible banana skins thrown at black people every day - Barnes
- Subconscious racism will remain in football for a long time - Onuoha
Manchester City welcomed Chelsea's decision to issue suspensions.
A club statement said: "The club and Raheem are fully engaged with Chelsea FC and the investigating authorities as they continue to examine the events in question.
"Manchester City and Raheem are committed to working with all relevant parties and organisations to support the objective of eradicating racism from the game."
Social media users posted a video of an incident during which Sterling was shouted at as he collected the ball from behind the goal.
Sterling said he "had to laugh" when he heard the remarks because he expects "no better".
Colin Wing, 60, has said he is one of the fans who has been suspended but told the Daily Mail that, although he swore, he used the word 'Manc' rather than 'black'.
"I'm deeply ashamed by my own behaviour," he said. "I want to apologise unreservedly to Raheem and hope he can be a better man than I am by accepting it.
"Even if it wasn't racist, it's not right what I said. Even the swearing is bad - but I got carried away. I was completely out of order."
Another fan, who gave his name as 'Dean', called Talksport on Monday to apologise. He added: "I didn't say anything racist, but I do admit swearing at him and calling him an embarrassment to England. I don't defend it."
An Instagram post by Sterling after Saturday's match saw him question the way the media portrays black players and has prompted debate between stakeholders in the game.
The Professional Footballers' Association has said negative press coverage of Sterling "emboldens racist rhetoric", adding the former Liverpool player is "often singled out".