Galatasaray said they would "initiate criminal proceedings" against Fenerbahce manager Jose Mourinho after claiming he made "racist statements" following the teams' 0-0 draw on Monday.
It was not clear which statements Galatasaray were referring to.
Speaking in the news conference after the Istanbul derby, Mourinho said the home bench had been "jumping like monkeys" and also repeated his criticism of Turkish referees, saying it would have been a "disaster" to use an official from the country.
Monday's match was refereed by Slovenian Slavko Vincic after both clubs requested a foreign official take charge of the fixture.
As well as the threat of legal action, Galatasaray said they would submit "official complaints" to football's governing bodies.
Mourinho - a former Chelsea, Manchester United and Tottenham manager - and Fenerbahce are yet to respond to the accusations.
After the game, Mourinho was asked about the performance of 19-year-old defender Yusuf Akcicek and said: "I have to thank the referee. After the big dive in the first minute and their bench jumping like monkeys on the top of the kid... with a Turkish refer,e you would have a yellow card after one minute and after five minutes I would have to change him."
He added: "I went to the referee's dressing room after the game, of course, the fourth official was there, a Turkish referee. I told him 'thank you for coming here, you come for a big match' and I turned myself to the fourth official and I said 'if you were a referee this match would be a disaster'."
In a statement, Galatasaray said: "Since the commencement of his managerial duties in Turkey, Fenerbahce manager Jose Mourinho has persistently issued derogatory statements directed towards the Turkish people. Today, his discourse has escalated beyond merely immoral comments into unequivocally inhumane rhetoric.
"We hereby formally declare our intention to initiate criminal proceedings concerning the racist statements made by Jose Mourinho, and shall accordingly submit official complaints to Uefa and Fifa.
"Furthermore, we shall diligently observe the stance adopted by Fenerbahce - an institution professing to uphold 'exemplary moral values' - in response to the reprehensible conduct exhibited by their manager."
Two-time Champions League winner Mourinho, 62, was appointed Fenerbahce manager last summer and was banned and fined earlier this season for condemning refereeing standards in Turkey.
Before Monday's game he had welcomed the decision to use a foreign official after previously describing the environment in the country as "toxic".
"I think it's important for the credibility, for the image of the match," Mourinho said.
BBC Sport has contacted Fenerbahce for comment.
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