The spat boiled up after Preciado was incensed by Mourinho's suggestion that Gijon had not made a serious attempt to beat Barcelona earlier this season and said the Portuguese had shown a lack of respect.
He made disparaging remarks about Mourinho at a news conference, prompting Real to release a statement before their match at the Molinon stadium in Gijon at the weekend condemning his comments.
Spain's state commission against violence, racism, xenophobia and intolerance in sport said after a meeting in Madrid on Thursday the row had risked creating a hostile atmosphere around the fixture, which Real won 1-0.
"In the light of articles published in certain media on the exchange of statements by the coaches... the commission agreed they could have contributed to the creation of a hostile climate," said a statement posted on the website of the government sports council on Thursday.
"The commission also believes that it is necessary to prevent this kind of situation happening again," the statement said, adding the Spanish football federation (RFEF) had been asked to take appropriate disciplinary action against the pair.
Several La Liga coaches, including Villarreal's Juan Carlos Garrido and Espanyol's Mauricio Pochettino, backed Preciado, whom local media said clashed with Real officials as they were leaving the stadium after the match.
In a statement on their website on Thursday, Real expressed their "profound opposition" to, and "disappointment" with, the commission's ruling and director general Jorge Valdano called a news conference to address it.
Mourinho had made his comments in an effort to promote the "sporting spirit" that should be present in every match and to "keep the competition clean", the statement said.
EXAGGERATED POLEMICS
Valdano added: "Our coach made some comments putting across clear arguments whereas Preciado answered with defamatory remarks that were out of line.
"It's a big mistake to lump the two coaches together for their remarks.
"I sincerely believe that Mourinho replied putting his arguments in context which up to now have not been disproved.
"We are a very big focus for the media and so is Mourinho. This can provoke exaggerated polemics around the personality of Mourinho and what Real Madrid represents."
In a statement on their website, Gijon said they regretted the disagreement between the two coaches and had considered the matter closed.
However, they said Real's latest statement and Valdano's comments at his news conference had been "unfortunate" in that the club and their director general had set themselves up as the "judge" in the case.
"It must be noted that the origin of the polemic was in inappropriate and repeated comments made by the Real Madrid coach, Jose Mourinho," the club added.
"As well as offering all its support and consideration to our coach Manuel Preciado, Sporting will make itself fully available to the state commission aga
