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 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.
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."
"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
