Spanish football federation president Luis Rubiales
Rubiales, 46, has been widely criticised after he kissed player Jenni Hermoso on the lips following Spain's Women's World Cup final win last month.
Rubiales has repeatedly refused to resign over the kiss, which Hermoso said was not consensual.
The men's side have expressed their "regret and solidarity with the players whose success has been tarnished".
"We want to reject what we consider unacceptable behaviour on the part of Mr Rubiales, who has not lived up to the institution he represents," said forward Alvaro Morata in a statement on behalf of the Spain squad.
"We firmly and unequivocally stand on the side of the values that this sport represents.
"Spanish football must be a driving force for respect, inspiration, inclusion, and diversity and must set an example with its behaviour both on and off the field."
Luis de la Fuente, head coach of the men's team, last week asked for "forgiveness" after initially applauding a speech in which Rubiales said he would not resign.
De la Fuente added he would not step down from his job.
After Spain's 1-0 victory over England at Sydney's Stadium Australia on 20 August, Rubiales also grabbed his crotch while celebrating in the VIP area, with Queen Letizia of Spain and her 16-year-old daughter standing nearby.
He has been provisionally suspended by world governing body Fifa and Spain's national sports tribunal (TAD) has opened a misconduct case against him.
On 1 September, Rubiales acknowledged he had "made mistakes" but repeated his belief that the kiss was consensual.
He added: "I will continue to defend myself to prove the truth."
After calling a press conference, Morata read out the statement alongside fellow senior players Marco Asensio, Cesar Azpilicueta and Rodri.
"We want to convey, once again, our pride and heartfelt congratulations to the women's national team for winning the World Cup in Sydney," he said.
"It's a historic milestone filled with significance that will mark a before and after in Spanish women's football, inspiring countless women with an invaluable triumph.
"Therefore, we want to express our regret and solidarity with the players whose success has been tarnished."
Spain's squad have gathered for a training camp before Euro 2024 qualifying matches against Georgia on Friday and Cyprus on Tuesday, 12 September.
"We would like to focus on sporting matters from now on, considering the importance of the challenges ahead," added Morata.
On 28 August Spanish prosecutors opened a preliminary investigation into whether the incident amounts to a crime of sexual assault, while the regional leaders of the Spanish football federation (RFEF) called for Rubiales' resignation.
His mother locked herself in a church on the same day and went on an "indefinite" hunger strike in protest against the treatment of her son. She was taken to hospital two days later and discharged the following day.
The head of Spain's Olympic Committee Alejandro Blanco has said Rubiales' actions were "inappropriate and unacceptable", but an "isolated incident" that did not represent Spanish sport as a whole.
The RFEF is also exploring its options over whether it can sack Women's World Cup-winning head coach Jorge Vilda.
Vilda is still in his post despite most of his coaching staff resigning in protest against Rubiales' refusal to quit, while 81 female players, including all 23 World Cup winners, have said they would not play for the team again while Rubiales remained in his role.
A video has also emerged appearing to show Hermoso and her team-mates laughing and discussing the kiss on the team bus following the game.
Hermoso appears to be viewing a meme of ex-Spain men's goalkeeper Iker Casillas kissing his then-partner Sara Carbonero, a television presenter, during an interview following the country's 2010 World Cup victory.
The 33-year-old, who plays for Mexican side Pachuca, later says "he comes over and hugs me like this" when talking about Rubiales.
In her statement denying the kiss was consensual, Hermoso said: "I feel the need to report this incident because I believe no person, in any work, sports or social setting should be a victim of these types of non-consensual behaviours.
"I felt vulnerable and a victim of impulsive-driven, sexist, out-of-place act, without any consent on my part. Quite simply, I was not respected."
She added she was put "under continuous pressure" to help with a "statement that could justify" Rubiales' actions - and so were her family, friends and team-mates.
-- Courtesy of BBC Sport