Real Madrid said it "firmly rejects "having a regular-season Spanish league game played in the United States and warned of "a turning point in the world of football".
Villarreal, in contrast, is promising free travel and tickets for season-ticket holders if its match against Barcelona in Miami is approved, in what would be a first for the league. The 17th-round match in La Liga would be played at the Hard Rock Stadium.
Madrid said Tuesday it has taken action to keep the Dec 20 match from happening, claiming it would hurt the "integrity of the competition" and the "legitimacy of the results".
"The measure, which was taken without prior information or consultation of the clubs participating in the competition, infringes the essential principle of territorial reciprocity, which applies in two-legged league competitions (one match at home and the other at the home of the opposing team), upsetting the competitive balance and giving an undue sporting advantage to the applicant clubs," Madrid said.
The club said the match would set "an unacceptable precedent that opens the door to exceptions based on non-sporting interests, clearly affecting sporting integrity and risking the adulteration of the competition".
"If this proposal were to be carried out, its consequences would be so serious that it would be a turning point in the world of football," Madrid said.
The club said it has asked FIFA, UEFA and Spain's top sports body to not authorize the game in the US. The Spanish soccer federation on Monday approved a request for the match to be played in Miami. UEFA and FIFA now have to approve the request before it can be made official.
"Any modification of this nature must, in any case, have the express and unanimous agreement of all the clubs participating in the competition, as well as strictly respecting the national and international rules governing the organization of official competitions," Madrid said.
Madrid and Spanish league president Javier Tebas have often been at odds on various issues.
The club said UEFA should deny the request to play the game abroad based on the "criterion established in 2018 that prevents official matches in domestic competitions from being played outside national territory, except in duly justified exceptional circumstances, which are not present here".
Madrid said it asked the country's high sports council "not to grant the necessary administrative authorization without such unanimous consent".
"Real Madrid reaffirms its commitment to respect the national and international rules that guarantee the fairness and proper functioning of official competitions, and will defend its compliance with them before all competent bodies," the club said.
Earlier on Tuesday, Villarreal said its season ticket-holders can travel for free and receive free tickets for the match. It said those who don't want to go, or can't go, will get a 20 percent discount on their season tickets.
"We would be the first (Spanish) team to play a league match abroad," Villarreal president Fernando Roig Alfonso told a news conference. "It would greatly help us expand our brand in a key market like the United States."
Staging a match abroad has long been part of the league's goal to promote soccer and its brand in other countries.
It first tried to stage a match in the US in 2018, with a game between Barcelona and Girona, but the idea was dismissed after criticism from players, fans and clubs. Subsequent attempts to play there also failed.
In 2018, the league had offered compensation packages for Girona fans.