The RFEF issued a statement on Thursday saying that 15 players had threatened to stop representing the national team if Vilda was not fired.
"We, the players, lament, in the first place, that the RFEF has made public, in a partial and interested way, a private communication, with information that affects our health - which is part of our privacy - sent in response to the request of the own Federation to know which of us wanted not to be summoned," they said in a joint statement on social media.
"Communication to which, by the way, we have not received a formal response," they added.
"We have never asked for the dismissal of the coach as has been commented. We understand that our job is not in any case to choose said position, but to express in a constructive and honest way what we believe can improve the performance of the group."
According to sources close to the situation, the players are unhappy with the management of injuries, the atmosphere in the locker room, Vilda's team selection and his training sessions.
The RFEF, which did not disclose the identities of the 15 players, said it fully supported the coach and that the players will only return to the team if they "recognise their mistake and ask for forgiveness".
"The RFEF is not going to allow the players to question the continuity of the national coach and his coaching staff, since making those decisions does not fall within their powers," it said, adding that refusing to honour an international call-up was a "very serious infraction" which can be punished by a suspension of between two and five years.
Vilda is due to announce next Friday his 23-player squad for friendlies against Sweden and the United States next month.
