Spain's prime minister says Luis Rubiales kissing Jenni Hermoso on the lips was an "unacceptable gesture" and that his apology is "not enough".
Spanish football federation president Rubiales kissed forward Hermoso following Spain's 1-0 win over England in Sunday's Women's World Cup final.
Rubiales apologised on Monday and said he was "completely wrong".
"What we saw was an unacceptable gesture," prime minister Pedro Sanchez said on Tuesday.
"Rubiales' apologies are not enough, I even think they are not adequate. He has to continue taking steps to clarify what we all saw.
"The players did everything to win but Rubiales' behaviour shows that there is still a long way to go for equality."
Spain's second deputy prime minister, Yolanda Diaz, Spain's called for Rubiales' resignation.
"Their excuses are useless," she said."[The Spain squad] have shown us many things about equality, not only in sports and football.
"They have shown us that there is still a lot to do in our country, that there is still a lot to do so that men and women can become equal."
The Spanish football federation (RFEF) has called an extraordinary general assembly "as a matter of urgency".
Hermoso said on Instagram that she "didn't like" Rubiales' actions after the final, but a statement released later on the Spain forward's behalf defended him.
In a video released on Monday, Rubiales said: "It was without bad intention at a time with a lot of excitement. In the moment, we saw it as natural, but outside a commotion has formed.
"I have to apologise, learn from this, and understand that when you are president you have to be more careful."
Rubiales has also been criticised by other Spanish government ministers and came under fire on social media for grabbing and kissing Hermoso.
Spain's equalities minster Irene Montero said: "It's a form of sexual violence women suffer on a daily basis", while sports minister Miquel Iceta told Spanish public radio it was "unacceptable" for Rubiales to kiss Hermoso.
Video footage circulated online after the match also showed Rubiales, who was sat in the VIP area of the stadium near Fifa president Gianni Infantino and Queen Letizia of Spain, grab his groin as he celebrated the final whistle.
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