"This disciplinary body considers the initiation of disciplinary actions pertinent to discover the nature and scope of the events and, if necessary, the corresponding sanctions if justified," the RFEF said in a statement.
The federation's competition committee will "initiate an extraordinary disciplinary procedure on Club Deportivo Eldense, as well as on each and every one of the players, coaches and delegates of the club", the statement continued.
Five members of the club, including coach Filippo di Pierro, two players, another member of the coaching staff and an Italian investor, who recently became Eldense's major shareholder, have been arrested by police on suspicion of corruption.
Eldense player Cheikh Saad was the first to point the finger at a number of his teammates and coach after their record-equalling defeat in Spain's third tier Segunda Division B on Saturday.
Saad told radio station Cadena Copa that certain players stood to make "huge sums" of money from bets placed on the match.
Club president David Aguilar then reported his suspicions to police and Spanish football authorities.
Di Pierro was appointed coach after an Italian investor took control of the club earlier this season with suspicions now raised over whether that investment was linked to illegal betting patterns.
"At the very least we must investigate it because there are certain links to an Italian group that has the look of what may be indications of an international betting ring when it comes to fixing matches," president of the Spanish league Javier Tebas said on Monday.
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