A series of meetings have been scheduled for Friday, Saturday and Monday at the offices of the LFP, who represent the 42 professional football clubs that make up La Liga and the second division.
Time is tight if the sides are to prevent a fixture backlog in a calendar with few spaces available to reschedule matches.
The international Euro 2012 tournament starts in June and prevents them simply rolling back the existing La Liga timetable past its current end date of May 13.
The AFE, who are demanding greater protection for players' wages at clubs who have gone into financial administration, last week called a strike for the first two rounds of matches in the top two leagues.
The AFE say around 50 million euros is owed by clubs to more than 200 players, and that a proposed emergency fund of 40 million euros put forward by the LFP was not enough.
The first meeting between the sides on Wednesday ended quickly with no resolution.
The strike action covers Friday to Monday inclusive over the next two weekends.
Some clubs have put out statements saying training had been suspended until Tuesday next week.
Real Madrid have scheduled a session on Friday afternoon and Barcelona said Monday's friendly against Napoli would go ahead as planned.
