Leaders of the Royal Spanish Football Federation said his “unacceptable behaviours” have “seriously damaged the image of Spanish football” following a meeting on Monday.
A High Court preliminary investigation is underway on whether Mr Rubiales committed an act of sexual aggression on Spanish player Jenni Hermoso when he grabbed her head and kissed her on the lips after Spain’s victory in the World Cup.
The prosecutor’s office said the court had received several complaints but would launch a full inquiry only if Ms Hermoso sought one.
It comes as hundreds of people protested in Spain’s capital Madrid on Sunday in support of Ms Hermoso as Mr Rubiales refused to step down, claiming the kiss was consensual.
Ms Hermoso said it was unwanted and demeaning. Spain‘s World Cup win has been tarnished by the fallout, coach Jorge Vilda said.
People called for Mr Rubiales’ resignation, chanting: “It’s not a kiss, it is aggression.”
The president was suspended by FIFA on Saturday amid outcry over the incident which was broadcast live following the final in Sydney on August 20.
The situation has fuelled a national row over women’s rights, macho behaviour and sexual abuse.
In a statement released on Monday the federation said: “The presidents request that Mr Luis Rubiales immediately present his resignation as president of the RFEF.
“We will urge the corresponding bodies to carry out...restructuring in strategic positions of the federation to give way to a new stage of management in Spanish football.
“Once FIFA suspended Mr Luis Rubiales, the federation’s internal protocols have been activated as a result of the suspension.
“The RFEF maintains its commitment to continue implementing its investment, as well as equality policies for the development of women’s football.”
The Sports Administrative Court was due to decide whether to take up a case against Rubiales after an extraordinary meeting on Monday.
Acting Labour Minister Yolanda Diaz said that Rubiales’ defiance and the support from some federation members showed that macho behaviour was systemic in Spanish society.
“What footballer Jenni Hermoso experienced should never have happened,” Ms Diaz said in a video statement prior to a meeting with the women’s players’ union.
United Nations spokesperson Stephane Dujarric said on Monday that sexism was still a critical issue in sport and urged the Spanish authorities and government to deal “with this in a manner that respects the rights of all female athletes.”
“How difficult is it not to kiss somebody on the lips? I don’t see any indication that anything was consensual,” she added.
Meanwhile Mr Rubiales’ mother locked herself inside a church and started a hunger strike to protest against her son’s treatment.
All 23 players on Spain’s cup-winning squad including Ms Hermoso, as well as dozens of other squad members, said on Friday they would not play internationals while Mr Rubiales remained head of the federation. Their next match is away to Sweden in the Nations League on September 22.
At a federation meeting on Friday where he had been widely expected to step down, Mr Rubiales refused to quit, seeking to defend his behaviour and calling the kiss “spontaneous, mutual, euphoric and consensual.”