Cardiff City want an apology from Reading after events that led to four Bluebirds fans being arrested by Thames Valley Police during their 1-1 FA Cup draw at Madejski Stadium on Saturday.
The force said the four were arrested for "alleged racially aggravated abuse" and later released under investigation.
Cardiff dispute those allegations.
They said: "Language could be heard taking place between fans of both clubs and was of an anti-Welsh/anti-English nature".
The statement added: "We are extremely disappointed that Reading Football Club chose to label the behaviour as racist and homophobic.
"We also question their protocol and procedure on the day and welcome a full investigation into its use for the benefit of both our clubs and indeed British football."
Fans' chants led to a public address warning to Cardiff fans during the match.
Cardiff chief executive Ken Choo said in the statement on Monday: "The announcement made at Reading this weekend was both damaging and hurtful and we would welcome a public apology from them to our supporters."
He added: "Our football club prides itself on its respect of all people, irrespective of their background, beliefs or orientation.
"Cardiff is a diverse and welcoming, modern multicultural city and our supporters' actions reflect that at our games.
"We have a zero tolerance approach towards racist or homophobic behaviour and our supporters' conduct consistently reflects that."
Choo is confident that after police conclude their investigation, "the reputation of our club and fans will be fully and unequivocally restored".
In their statement, Cardiff said: "It is understood that the four Cardiff City supporters arrested and subsequently released prior to investigation were cited during the fixture for using what could be considered as unwarranted language.
"This language could be heard taking place between fans of both clubs and was of an anti-Welsh/anti-English nature."
Reading have been asked to comment.
The Football Association is investigating and has asked both clubs for their observations.
The two clubs meet again on Friday night in the Championship at Cardiff City Stadium, with the Royals returning to the Welsh capital for the FA Cup fourth-round replay on Tuesday, 4 February.