La Liga president Javier Tebas has said the stabbing of two Paris Saint Germain fans after Wednesday's Champions League game at Barcelona showed how important it was to eradicate the threat of ultras.
The supporters were taken to hospital after being stabbed outside the Camp Nou by individuals wearing balaclavas and dark clothing, according to the local Mossos d'Esquadra police force.
Police sources told El Pais that the authorities were sure Barca's Boixos Nois ultras had been involved.
The stabbings came a week after the death of a Deportivo La Coruna supporter in a pre-organised fight with Atletico Madrid ultras before a game at the Calderon.
That incident led the La Liga authorities and Spain's sports minister to move to ban all radical fan groups throughout the country and clamp down on offensive chanting during games.
Tebas told AS that a comprehensive policy starting with a clampdown on chants inside stadiums was necessary because "verbal violence" could lead to physical violence.
"Words are what comes before the situation experienced at the Camp Nou," he said. "We are going for them. We are very clear at the LFP and at the clubs.
#INSERT type:image caption:Two PSG fans were stabbed near the Camp Nou after a Champions League match. END#
"We are going to eliminate the ultras from football -- those who assault, those who insult, those who disparage and those who are intolerant."
The Boixos Nois were involved in a number of violent incidents before being banned from the Camp Nou by former Barca president Joan Laporta in 2003.
Laporta's successor Sandro Rosell made reported moves towards allowing the group back into the stadium, but police vetoed the suggestion.
That has meant members of the group cause trouble at away games, Mossos director Albert Batlle told Catalunya Radio.
Barcelona and Real Madrid were charged earlier this week over offensive chanting from supporters during games last weekend.
Madrid president Florentino Perez was reportedly unhappy at the charge, because Real have been working hard to remove Ultras Sur from the Bernabeu, as a result of which he had received threats.
Speaking at a Christmas dinner, he said he was committed to ensuring that violent individuals had no place at the club, adding: "Real Madrid has a zero tolerance policy for violent people."
Officials at Atletico Madrid say the club has cut all ties with the Frente Atletico group of ultras, although some members of the group were photographed at Tuesday's Champions League game at Juventus.