Only hours after the head of the Spanish soccer federation insisted he would not step down for grabbing and kissing a member of Spain’s winning team fully on the lips at a Women’s World Cup medals ceremony last weekend in Australia, players on the squad announced on Friday that they would refuse to play until he was gone.

In a joint statement issued through their union, dozens of players said they would not take the field to play for Spain “if the current managers continue.”

In the statement, the player kissed, Jennifer Hermoso, said that “at no time did I consent to the kiss that he gave me.”

The players’ ultimatum came after Luis Rubiales, president of the Royal Spanish Football Federation, said at a news conference that he would not step aside, arguing he was the victim of “social assassination.”

News reports had predicted that Mr. Rubiales would quit after five years at the helm of Spanish soccer, but he instead took a defiant stand.

“I will not resign,” he said several times at an extraordinary meeting of the federation, to loud applause from some and silence from others, adding that “I will fight this to the end” and accusing his critics of “false feminism.”

In their response, the players say they condemn “behaviors that have violated the dignity of women,” and that they expected “forceful answers from the public powers” to address the incident.

The government is limited in its ability to punish members of the soccer federation, but after Mr. Rubiales made his remarks on Friday, it said it was taking steps to have him suspended. Víctor Francos, president of the National Sports Council and secretary of state for sports, said on Cadena SER radio: “We’re going to act — we’ve activated all the mechanisms to take appropriate measures.”

The controversy was a reminder that despite the Spanish team’s steep trajectory into the highest echelons of women’s soccer — the team did not qualify for a Women’s World Cup until 2015 — the program has been dogged by sexism and other scandals.

Most recently, 15 players revolted last year against the coach, Jorge Vilda, and the federation led by Mr. Rubiales. They complained of outdated training methods and controlling behavior, and refused to play for the national team, although some of them returned and played in the World Cup.

Players on the women’s national team have also said that they have been disrespected by top male soccer executives, saying that the men’s team was given superior equipment and treatment. Mr. Vilda has emerged as a polarizing figure in Spanish soccer, but Mr. Rubiales thanked him effusively on Friday and said that he would be rewarded with a new contract.