Spanish players union calls off strike
The AFE had officially called for industrial action over unpaid wages, particularly in the third and fourth tiers of the game, that would affect matches across the top four leagues between April 16-19.
"There is a solid agreement," Lissavetzky was quoted as saying on the El Pais website.
"It establishes the bases for the future to continue moving forward, in which everyone has had to give ground."
Advances were made in talks on Monday between the AFE, the league, the federation and the government and the outlook had been positive for the return to the negotiating table on Tuesday.
The strike would have affected the matches between La Liga leaders Barcelona and city rivals Espanyol, and second-placed Real Madrid and Valencia, among others.
It would have placed additional strain on a calendar that is already tight because of this year's World Cup.