After a meeting in Madrid on Friday, the LFP, which represents first and second division clubs, said it wanted the rule dropped for the start of the 2012/13 season so clubs were in a stronger position to negotiate rights with television companies.
The league also wants guarantees about how much cash they are entitled to receive from betting and lottery revenue.
Free matches would not necessarily be stopped entirely but the LFP wanted the obligation to show them to be dropped, president Jose Luis Astiazaran said at a news conference.
"We discussed the obligation for free games, which does not mean there won't be any, rather that we do not want the obligation to exist," Astiazaran explained.
"We will set a timeframe for talking to the government and parliamentary groups but if there is no conclusive progress matchday 30 (on April 2/3) will not be played," he added.
"If that is the case, that matchday would be moved forward a week and the league would end in June."
On the weekend when the strike would take place Barcelona are scheduled to visit Villarreal while Real Madrid are due to host Sporting Gijon.
In a statement later on Friday, the LFP noted that Spain was the only country in the world in which one match had to be shown for free, which it said constituted "the expropriation of the clubs' rights with no recompense whatsoever".
The rule was introduced in 1997 at a time when fans had to pay significantly more to watch matches on pay television than was now the case, the statement added.
The LFP said its stance had the "unanimous support" of the European Professional Football Leagues (EPFL), who considered that the rule "affected the sustainable development of the Spanish league, its economic viability, sporting success and social function," the LFP said.
