Spain’s record scorer Jenni Hermoso says her international team-mates are “living through the worst moment” in women’s football.
The RFEF said the players claimed Vilda’s tenure was affecting their emotional state and health.
Spain’s players later denied they had called for Vilda to be sacked.
The players – who were not named by the RFEF – also said they were disappointed the federation had made their “private communication” public.
Hermoso, 32, who made her debut for the national team in 2011, has released a statement on social media saying: “These last few days, without a doubt, have been some of the most difficult that I have lived as a professional footballer and as a member of the Spanish national team.”
The striker, who joined Pachuca from Barcelona in the summer, said she wished the situation “had never been made public” but she respected the decision of her colleagues to express themselves.
‘Not blackmail’
Hermoso said she wanted to “publicly express my unconditional support” to all her team-mates who wanted to speak out about the “need to improve the working conditions” within the national team.
“Not only do I understand their reasons, but I have also experienced many of the same feelings and concerns,” she wrote.
“I am very aware of this because I have had the opportunity to live unique and immensely happy experiences playing for Spain, but I have to admit that in recent years I have also had very tough moments of suffering before, during and after national team camps; an endless number of situations that left me unable to recognise myself and in turn made me feel immense loneliness within the national team.”
She said the growth in women’s football must be accompanied by “adequate professionalisation” but the disconnect between the coach and players and the federation and players were “signs that something is not working”.
“The reality is that I haven’t slept for days, thinking of solutions, and looking for explanations to the great emptiness that I feel inside.
“After all that we have worked for, it breaks my heart to realise that we are living through the worst moments in the history of women’s football in Spain.”
Hermoso said she didn’t know what the solutions were, but she was clear the players’ action was “not blackmail, nor is this happening on a whim”.
Spain are due to play their next match on 7 October with an international friendly against Sweden, followed by the visit of world champions USA four days later.
Vilda, 41, has been the national team coach since 2015 and led his side to the quarter-finals of Euro 22, where they lost to eventual winners England.