The majority of Spain's World Cup-winning squad will continue their boycott of the national team until further changes are made, saying they do not yet "feel in a safe place".
Last month's win was overshadowed by the federation's president Luis Rubiales kissing forward Jenni Hermoso after the final.
The fall out eventually led to Rubiales' resignation.
But a total of 39 Spanish women's players say more needs to be done.
The Spanish football federation later on Friday expressed their commitment to change being made "to restore the functioning of the entity".
That came after a statement by the Spain players, which includes 21 of the 23 members of the World Cup-winning squad, read: "The changes that have occurred are not enough for the players to feel in a safe place, where women are respected, where there is a commitment to women's football and where we can give our maximum performance.
"The players of the Spanish team are professionals, and what fills us most with pride is wearing the shirt of our team and always leading our country to the highest positions.
"For this reason, we believe that it is time to fight to show that these situations and practices have no place in our football or in our society and that the current structure needs changes.
"We do it so that the next generations can have a much more equal game that we all deserve."
According to the statement, the players are calling for:
A restructuring of the Spanish football federation
Resignation of the temporary president
A different organisation of women's football, new general secretary and presidency cabinet
A new media department
New thinking about the integrity department
The Spanish football federation said: "The Federation wants to reinforce its commitment to the world champions, for whom it feels enormous pride. "It is essential that international organisations, the media and society understand this and help us do so. A lot is at stake and we must be aware."
Spain head coach Jorge Vilda, who was considered a close ally of Rubiales, was sacked last week.
His successor, Montse Tome, was due to pick her first squad on Friday for upcoming Nations League matches against Sweden and Switzerland, but a news conference scheduled for 15:00 BST was postponed.
Most of Vilda's coaching staff resigned and some 81 players refused to play for Spain until Rubiales stepped down, which he did on Sunday.
Tome, who was Vilda's assistant manager, has become the first woman to hold the position of Spain women's boss.
The Spanish government has assured players that changes will be made and there will be a greater representation of women in the Federation.
Rubiales has been banned from going within 200m of Hermoso, who has said the kiss was not consensual, after the 33-year-old filed a legal complaint last week.
Appearing in court for the first time on Friday, Rubiales denied sexually assaulting Hermoso.