Tebas wrote earlier on Friday on social media that "Real Madrid’s management directs an orchestra of mouthpieces and Real Madrid TV leads the singing."
The LaLiga president was responding to articles by two journalists saying he and LaLiga were acting against Real's interests.
Tebas added that the authors in the El Debate newspaper were amplifying a message on behalf of Real's management. Reuters has asked El Debate for comment.
Tebas on Friday criticised Real Madrid TV's coverage of officiating at their matches.
"Their score is always the same: select the plays that suit them, repeat the grievance, feed the suspicion, and point fingers at the enemies," he wrote.
"That method recalls propaganda mechanisms used by Goebbels, Nazi Germany's Minister of Propaganda.
"The comparison is with those propaganda techniques, not with an ideology or, of course, with the Madridista fanbase," added LaLiga's president.
The comments have deepened a feud between the club and La Liga's chief.
Real in September called for a new LaLiga president in response to Tebas calling their complaints about refereeing decisions 'a smokescreen' for their shortcomings on the pitch.
The club have now released a statement demanding that Tebas resign from his positions as LaLiga chief and vice-president of the Royal Spanish Football Federation.
The statement called it "intolerable and extraordinarily serious" that Tebas used "a comparison with the propaganda methods of the Nazi regime to discredit our club, its management and its television.
"Tebas' repeated conduct demonstrates a lack of neutrality, respect and impartiality incompatible with his institutional responsibilities," said Real.
"It is unacceptable that he even takes advantage of questions, information or opinions from journalists unrelated to the club to direct his accusations at us, attributing to us actions of third parties for which we bear no responsibility."
The 64-year-old Tebas, who is elected by the 42 professional clubs in Spain's top two tiers, has been LaLiga president since 2013. In 2023, he was re-elected unopposed until 2027.
Real Madrid's statement came hours after LaLiga confirmed that they are one of the six clubs that will sit on the league's Executive Committee this season.