"We haven't reached any kind of agreement," LFP president Jose Luis Astiazaran, whose organisation represents the 42 professional clubs in the top two divisions, told reporters after the first meeting since the strike was invoked last week.
"The AFE have dug their heels in. There are important differences but we will have to continue moving forward."
The Union have called a strike for the first two rounds of matches in the top two leagues, which are scheduled to kick off on Saturday, demanding greater protection for players' wages at clubs who have gone into financial administration.
The Union have said at the end of last season around 50 million euros was owed to 200 players, and that a proposed emergency fund of 40 million euros put forward by the LFP was not enough.
Astiazaran continued: "We are in agreement on 80 percent of the questions and it's a shame that for 20 percent we have found ourselves in this situation.
"We have achieved much recently... however, it is impossible for the first round of matches not to be affected by the strike."
STRIKE UNJUSTIFIED
In a separate statement issued later, the league blasted: "THIS STRIKE IS ABSOLUTELY UNJUSTIFIED but is also STERILE, because the LFP has gone as far as it is able to."
Representing the AFE, Luis Gil said: "The league doesn't want to bridge the gap. The biggest problem is that the players want guarantees they are going to get paid because there are more than 200 who are owed money.
"At present the AFE are not considering extending the strike action beyond the second round of matches. We want the law applied that clubs who do not pay should be relegated."
Neither Barcelona or Real Madrid, who face off in the second leg of the Spanish Super Cup at the Nou Camp later on Wednesday, were prepared to make an official comment on the strike.
Valencia president Manuel Llorente told reporters: "It's a decision by the players and I don't think it is adequate. There are other ways to resolve this. What the AFE is asking is impossible. It is going to be a very difficult negotiation."
Llorente said reform of the application of the law known as 'ley Concursal' in sport, whereby clubs can voluntarily go into administration to seek protection from creditors, was the real problem that needed addressing.
EASY WAY OUT
The judges appointed to administer the clubs can override competition rules that could lead to a club being relegated for failing to honour its commitments during the process.
Analysts have said clubs have abused the rules surrounding ley concursal as an easy way out of their self-inflicted difficulties and to avoid possible relegation.
A growing number of Spanish clubs have slipped into financial difficulties recently.
Racing Santander were the latest La Liga side to seek protection from creditors, joining Real Mallorca, Real Zaragoza and the three promoted teams - Real Betis, Rayo Vallecano and Granada - in administration.
A recent study by an accounting professor at Barcelona University, Jose Maria Gay, showed the 20 top-flight clubs made a combined net loss of some 100 million euros in the year to the end of June 2010, up from 19 million the previous year.
The total debt at 3.43 billion euros was more than double revenues of 1.61 billion euros.
