The AFE said in a statement on Monday it wanted to continue talks with the sports council, the football federation and the professional league to agree a "grand pact for Spanish football" that would satisfy the players' demands.
If an accord was not reached, all players in the top four tiers would go on strike for the April 16-19 matches and did not rule out further action, the statement said.
Under new president Luis Rubiales, the AFE is taking a more active approach to helping players get cash they are owed by financially struggling clubs, especially those working in the third and fourth tiers of Spanish football.
Rubiales is a former player at Valencia-based Levante and helped organise industrial action over unpaid wages in the 2007/08 season when they were in Spain's top division.
The April 16-19 strike, if it goes ahead, would affect the matches between La Liga leaders Real Madrid and third-placed Valencia and champions Barcelona and city rivals Espanyol, among others.
The AFE said a large majority of players backed Monday's statement.
