Chelsea banned four supporters this week pending a police investigation into alleged racial abuse of Manchester City forward Raheem Sterling in the sides' league fixture last weekend.
The Metropolitan Police also charged four men following incidents in the North London derby between Arsenal and Tottenham Hotspur earlier this month.
A banana skin was thrown on to the Emirates Stadium pitch by one supporter after Arsenal's Gabonese striker Pierre-Emerick Aubameyang had scored in the 4-2 win.
Anti-discrimination charity Kick It Out said last month that reports of discriminatory abuse within football were up 11 percent from last season.
The Premier League released a statement on Friday calling for respect.
"Some brilliant football has been played this Premier League season and the vast majority of fans have generated exciting and passionate atmospheres in stadiums. However, there have been incidents recently where a very small minority have behaved unacceptably," the statement said.
"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."
Some Chelsea fans were also alleged to have engaged in anti-Semitic chanting in their Europa League group game against Vidi FC in Budapest on Thursday.
The club said any supporters found guilty would face the strongest possible action. European soccer's governing body UEFA said they would wait to receive their official reports before launching an investigation.
"Anti-Semitism has no place in football. So we won't stop fighting it. We won't stop calling it out. We won't stop reporting it. And neither should you," Kick It Out told supporters on Twitter.
The Premier League said that any fans who witnessed unacceptable behaviour should report it to a steward or to Kick It Out.
(Reporting by Christian Radnedge; Editing by Toby Davis)
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