Gijon are 18th in La Liga, after losing seven of their last eight league games.
Abelardo, 46, a Gijon native, played for the club for five years and took over as head coach in 2014.
"I don't have a problem writing off the money," said Abelardo. "There are more important things - loyalty to my club above all."
The ex-Spain and Barcelona defender, who was in tears during the news conference, will be replaced by former Girona, Valladolid and Levante coach Rubi.
Abelardo has left his role as Sporting Gijon head coach, but refused a reported four million euros (£3.5m) in compensation.