UEFA said on Friday that the three clubs will face sanctions, and European soccer's ruling body has started disciplinary proceedings against them. Multiple sources told ESPN earlier this week that a maximum punishment under the organisation's disciplinary pathway would be a two-year ban from the Champions League or Europa League.
Nine other clubs, including six English Premier League teams, backed out of the plan and have signed a "Club Commitment Declaration" that includes a series of reintegration steps.
"The founding clubs have suffered, and continue to suffer, unacceptable third-party pressures, threats, and offenses to abandon the project," Real Madrid, Barcelona and Juventus said in a joint statement.
"....and therefore desist from their right and duty to provide solutions to the football ecosystem via concrete proposals and constructive dialogue.
"This is intolerable under the rule of law and Tribunals have already ruled in favour of the Super League proposal, ordering FIFA and UEFA to, either directly or through their affiliated bodies, refrain from taking any action which may hinder this initiative in any way while court proceedings are pending."
The nine clubs who pulled out of the Super League and are back in the UEFA fold have agreed to "take all steps within their power" to end their involvement in the breakaway league.
The Super League argued it would increase revenue for the top clubs in Europe and allow them to distribute more money to the rest of the game. UEFA, other teams and fan organisations, however, said the league would only boost the power and wealth of elite clubs.
The three teams' statement also added that one of its "main objectives" was to promote women's football despite there being no plan in place for a women's competition when the ESL was announced.
"Moreover, one of its main objectives was to promote women's football on a global level, a tremendous, but currently underestimated, opportunity for the sector," the clubs said.
Juve, Real and Barca said they were ready to reconsider the proposed approach of the breakaway project after the backlash but said it would be "highly irresponsible" for them to abandon the project.
"We are fully aware of the diversity of reactions to the Super League initiative and, consequently, of the need to reflect on the reasons for some of them," their statement added.
"We are ready to reconsider the proposed approach, as necessary.
"However, we would be highly irresponsible if, being aware of the needs and systemic crisis in the football sector... we abandoned such mission to provide effective and sustainable answers to the existential questions that threaten the football industry."
The nine clubs who pulled out have been handed financial punishments by UEFA and have agreed to make a combined €15 million goodwill contribution to benefit youth and grassroots football across Europe.
ESPN's Sam Marsden and Moises Llorens contributed to this report.