The LFP wants Spain's Socialist administration to scrap a rule that one La Liga game per matchday should be shown on free television, arguing the move would strengthen clubs' bargaining power in negotiations on audiovisual rights with media firms.
It also wants guarantees about how much cash it is entitled to receive from betting and lottery revenue.
The league, which represents first and second division clubs, has the backing of the Spanish football federation (RFEF) but six of 20 clubs in the first division - Sevilla, Villarreal, Athletic Bilbao, Espanyol, Real Zaragoza and Real Sociedad - filed a legal challenge in a Madrid court on Wednesday in an attempt to block the postponement.
The six oppose the LFP because they believe a strike would be "disproportionate, innoportune, against the interest of clubs, the competition and supporters and, what's more, against the law," Sevilla said on their website.
"It's not the right moment, politically speaking, to make these demands and, what's more, it should not be the fans who pay the price," Sevilla president Jose Maria del Nido was quoted as saying in local media.
On the weekend under threat, April 2/3, Sevilla are due to host Zaragoza, while La Liga leaders Barcelona play at Villarreal and second-placed Real Madrid host Sporting Gijon.
The LFP said on Tuesday the latest talks between league officials, the government and parliamentary groups had failed to produce any progress and it stood by its decision to strike.
The league has said the free game will not necessarily be dropped but it wants the obligation to show it to be removed.
An LFP spokesman said on Wednesday it respected the position of each of its members but would stick to the decision taken at a meeting last month to postpone games unless the government backs down.
Jaime Lissavetzky, secretary of state for sport, appealed for "common sense" and noted a television media law had been voted through a year ago without any of the political groups raising objections.
Speaking at an event in Madrid on Wednesday, he indicated he was "ready to listen and talk" to try to resolve the dispute.
Villarreal president Fernando Roig expressed support for the league's bid to get the free TV rule lifted but said a strike was the wrong way to go about it, especially at a time when the Spanish economy was struggling.
"It is not a good thing given what this country is going through at the moment for management to go on strike," Roig said on the club's website.
"I agree that the best way forward is through dialogue," he added. "I do not agree that the right path is a postponement."
According to Sevilla and Villarreal, if the April 2/3 games are postponed, they would be played on June 11/12, three weeks after the scheduled end of the season.
"If that happens I believe the final weeks of the league will be an authentic disaster," Roig said. "It seems to me a monstrosity and s
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