Real Madrid condemned racism from some of their supporters aimed at Barcelona players including teenager Lamine Yamal and Alejandro Balde during the club's 4-0 Clasico defeat on Saturday.
La Liga said they would report the incidents to Spanish authorities, while the government was also critical of the abuse.
"Real Madrid strongly condemns any kind of behaviour involving racism, xenophobia or violence in football and sport, and deeply regrets the insults that a few fans uttered last night in one of the corners of the stadium," said Los Blancos in a statement Sunday.
Videos emerged on social media after the game of racial abuse aimed at Barcelona players, with 17-year-old Spain star Yamal targeted during a goal celebration after becoming the youngest Clasico scorer.
The Spanish champions said they had "opened an investigation in order to locate and identify the perpetrators of these deplorable and despicable insults".
"La Liga will immediately report the racist insults and gestures directed at Barcelona players to the hate crime unit of the national police," said the Spanish top flight in a statement.
Spain's sports council (CSD) said their Commission against Violence, Racism, Xenophobia and Intolerance in sport would meet Monday to discuss the case.
"The Clasico is one of the greatest spectacles in the world, a true expression of the importance that football has in our country," said the CSD in a statement.
"In it, as in any other sporting event, there can never be any room for expressions of violence, racism, xenophobia, hatred or intolerance."
"Neither racism, nor insults, nor violence have a place in our country's sport," wrote Pilar Alegria, Spain's minister for education, professional development and sports on social media platform X.
Elma Saiz, Spain's minister for inclusion and migration, also offered support to Yamal.
"The racist insults aimed at Lamine Yamal in the Clasico are everything we in the government will fight against," she wrote on X.
"We will not allow attacks that we do not tolerate in other spaces to become normalised in sport."
Spanish football is struggling to combat racism in stadiums across the country.
Real Madrid striker Vinicius Junior has become a figurehead in the fight against racism and has been targeted on numerous occasions since arriving in Spain in 2018.
The Brazilian winger earned worldwide support in May 2023 when he squared off with Valencia supporters after suffering abuse at their Mestalla stadium.
In June three Valencia supporters were sentenced to eight months in prison as a result.
In January 2023, an effigy in a Vinicius shirt was found hanging from a bridge near the club's training ground alongside a banner saying: "Madrid hates Real".
In December, four Atletico Madrid fans were charged over the incident, with prosecutors pushing for jail terms of four years.
This week Spanish police arrested four men suspected of inciting an online hate campaign against Vinicius.
