The billionaire Blues owner spoke of a "battle" against antisemitism and invoked the horrors of the Holocaust as a reminder of the atrocities that can result from a failure to tackle hate.
Abramovich, who is Jewish, made the comments as Chelsea played US side New England Revolution in a friendly held as part of the London club's 'Say No to Antisemitism' campaign.
Writing in the programme, he said: "While people know us for our teams and our clubs on the pitch, sport is about far more than trophies. It is about ensuring our organisations play a positive role in all our communities.
"It has always been important to me to create a club that is welcoming to everyone - we actively celebrate our cultural and religious diversity.
"However, we are all too often reminded there is more to be done. The Holocaust was a crime without parallel in history.
"We must never forget such atrocities and must do our utmost to prevent this from ever happening again. And yet, around the world we are seeing a rise in instances of anti-Semitism."
The Blues squad visited Boston's Holocaust memorial on Wednesday ahead of the match at the Gillette Stadium, which is also home to the New England Patriots.
Chelsea have seen challenges in tackling cases of antisemitism by fans and they have been praised for their efforts in eradicating the issue.
The Blues launched their campaign in January 2018 to raise awareness and educate about antisemitism in football, vowing to take a zero-tolerance approach.
Calling for supporters to "join us in our battle against antisemitism", Abramovich said: "I am grateful to Chelsea fans and everyone who has supported us on this journey. With your help, we have been able to take a leading role in this vital area of work and demonstrate to everybody that we are a club open to all."