"Our players have won twice: first on the pitch, and now in giving a lesson to the world, a lesson of equality between men and women" Sanchez said.
Spanish midfielder Jenni Hermoso joined a mass strike of women players last week saying she did not consent to being kissed by the country's suspended football federation chief Rubiales after Spain's victory in the Women's World Cup final.
Sanchez, speaking in Malaga, applauded the players' stance.
Last week in a statement released by women players' union Futpro, Hermoso and 80 other players said they would not accept an international call-up "if the current leadership continues" at the Spanish football federation (RFEF).
Rubiales, 46, has defied expectations and refused to resign, provoking widespread indignation.
Sanchez said Spain was a feminist country, with women who had decided "to no longer submit. Never again. It's over" in reference to the slogan chanted in demonstrations in support of Hermoso.
On Friday, Spain's sports court agreed to investigate Rubiales for the forced kiss as the scandal-hit football chief insisted he would defend himself to "prove the truth".
The government lodged a complaint against Rubiales through the state-run National Sports Council (CSD) a week ago, accusing him of "very serious" offences.
In agreeing to take the case, the Administrative Tribunal for Sport (TAD) said it considered the behaviour in question "serious", falling short of the government's characterisation of Rubiales' actions.
Rubiales has been suspended by world governing body FIFA for 90 days while it decides on disciplinary measures.
Meanwhile, Veronica Boquete, a former national team skipper told AFP-TV in an interview on Saturday that the scandal was "the straw that broke the camel's back."
"It means that when there are no cameras, when there is no-one else, when it's not the final of a World Cup, a lot of other things happen, which we normalise and let pass when that shouldn't be the case," said the Boquete.
The 36-year-old, who plays in Italy with Fiorentina, was axed as skipper in 2017.
She hit out at the management of coach Jorge Vilda who took Spain to the World Cup title last month despite tensions between him and his players.