A Madrid court decided it was unable to resolve the union's dispute with the league about kick-off times on a day which is considered a holiday under a 2008 accord between the two organisations.
Under Spanish law, a different court should hear the case, judges Ricardo Bodas, Manuel Poves and Enrique De No Alonso-Misol said in a statement.
The ruling means Sunday's matches, including Barcelona versus Levante and Valencia against Espanyol, can go ahead as planned and the threat of postponement has been lifted.
AFE president Luis Rubiales told reporters the court had upheld the substance of the union's complaint and it would seek as much as 20 million euros from the LFP, equivalent to the amount the league said would be lost if the matches had to be postponed.
"In the past things were done the way the league wanted but that is over now," Rubiales said.
"If they (the LFP) fix the amount that would have been lost if we had not played on January 2 at 18-20 million then we will claim an amount along those lines," he added.
TV RIGHTS
Abdon Pedrajas, an AFE lawyer, said the union would recommend to its members that they play Sunday's matches.
However, the court ruling had established that the 2008 agreement that designates January 2 as a holiday had been violated and the union would therefore claim compensation in the relevant court, he added.
The important thing was that there would be football on Sunday, LFP president Jose Luis Astiazaran said.
"I congratulate everyone, especially club directors who have worked very hard to keep this calendar in place, which has been set since last June," he told reporters.
The row blew up last week after the LFP set the kick-off times for the January 2 fixtures between 4pm (1500 GMT) and 10pm local time.
The AFE initially said it wanted all five to start at 5 p.m. and later offered to play the matches on Monday.
However, changing the schedule would create problems for the LFP to fulfil its obligations to rights-holding television companies and it refused to back down.
The problem was partly caused by the practice in Spain of fixing kick-off times around 10 days before matches, unlike in rival European leagues where times are decided many months in advance.
