Tebas planned to draft a list of clubs that collaborate with radical "ultra" groups, and proposed sanctions including "points deductions or relegation."
The league, the national federation, and the committee for sports safety met on Thursday at the sports ministry to "consolidate the strategy for removing the ultras from our stadiums," he said.
The sports authorities said in a statement they decided to recommend fines of 60,000 euros ($74,270) and five-year match bans for the 88 fans it says were involved in a "brawl between radical fans" of Atletico Madrid and Deportivo La Coruna that resulted in the death of a 43-year-old Deportivo fan on Sunday.
The statement also said the upcoming 14th-round La Liga matches between Real Madrid vs. Celta Vigo, Barcelona vs. Espanyol, and Rayo Vallecano vs. Sevilla have been declared "high risk," and would likely require enhanced police surveillance.
Tebas said authorities were "preparing measures to curb verbal violence," which he said can lead to physical violence.
Tebas added the league fired former Deportivo la Coruna president Augusto Lendoiro after learning he attended the funeral of the hardcore ultra fan who died in a fight between rival supporters near Atletico's stadium in Madrid on Sunday.
Lendoiro was in May appointed a goodwill ambassador for Spain's league, and asked to promote the organization overseas after acting as president of Deportivo for 25 years.
Tebas said he was astonished to learn that more than 100 people attended the funeral of Francisco Javier Romero Taboada. The fan's coffin was draped in a radical group's flag, and flares and smoke fireworks were set off at the cemetery.
"I was very surprised to see Lendoiro at the funeral, so I made the decision to dismiss him," Tebas said, adding it was "not correct behaviour" from someone linked to the league.
"Going to a public event lends credibility, and acts as an apology to someone who came to Madrid with violence in mind," Tebas said, adding that Lendoiro's dismissal had not been hasty.
"There are decisions that do not require much thought," he said.