The AFE said on Monday they wanted a "grand pact for football" between players, clubs, the federation and the government that would satisfy their demands or they would stage a strike across the top four tiers of the league between April 16-19.
If it goes ahead, the action would affect the matches between La Liga leaders Real Madrid and third-placed Valencia and champions Barcelona and city rivals Espanyol, among others.
The LFP said in a statement on Tuesday such a move would damage the credibility of Spanish football, hurt clubs and players and place additional strain on a calendar that was already tight because of this year's World Cup.
"We are convinced that with calm, dialogue and compromise from all concerned we can avoid such negatives," they added.
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 AFE said on Monday a large majority of their members backed Monday's threat.
"If we have to go on strike we are all united," defender Manuel Pablo, captain of La Liga club Deportivo La Coruna, was quoted as saying in Marca sports daily on Tuesday.
"A large proportion of the inflation that is hurting the clubs is the fault of the players, who have dropped down into lower divisions with very lucrative contracts and try to keep the same level of income," he said.
