In a post on social media, Tebas accused Real Madrid of orchestrating a coordinated campaign against the league and its match officials.
The club's official television channel is known for showing compilations of errors made by referees who are set to officiate their upcoming games.
"The executive of Real Madrid has an orchestra of mouthpieces and Real Madrid leads the way," he wrote.
"Its script is always the same: select plays that favor it, repeat the alleged affront, increase suspicion and name enemies.
"It reminds one of the propaganda techniques that Goebbels used. The comparison is with the techniques, not with the ideology or, of course, with Madrid fans."
The response from Real Madrid was swift and uncompromising and, in an official statement, the club said Tebas's comments demonstrated he was unfit to continue in his role.
"Javier Tebas's repeated conduct demonstrates a lack of neutrality, respect, and impartiality incompatible with his institutional responsibilities," the club said.
"His constant attacks on Real Madrid and those demanding transparency and regeneration represent, in our club's view, a genuine scourge for Spanish football."
Real Madrid argued that Tebas's pattern of public criticism had eroded the neutrality expected of the head of Spain's top flight.
The club framed its demand for his resignation as necessary to protect the integrity of Spanish football and restore confidence in the league's leadership.
The exchange marks a significant escalation in the long-running tensions between Real Madrid and LaLiga's hierarchy.
While Tebas insisted his analogy referred solely to communication methods, the club viewed any invocation of Goebbels as beyond the bounds of acceptable discourse from the league's most senior official.
Jose Mourinho has admitted he would have forced his way out of Real Madrid if he were Vinicius Junior, pointing to the repeated abuse the Brazilian winger has suffered during his time in Spain.
Real Madrid believe Endrick has taken an important step in his development after the Brazilian forward delivered an impressive performance in a dramatic 4-3 Champions League victory over Roma.
Jose Mourinho has criticised the Spanish football authorities over their handling of Vinicius Junior's suspension after Real Madrid fought back from two goals down to beat Roma 4-3 in the Champions League.
Real Madrid produced a remarkable late comeback to beat Roma 4-3 at the Stadio Olimpico, scoring three times in the final stages to snatch victory after trailing 3-1.
