The incident happened as federation chief Luis Rubiales handed the Spanish team gold medals after they beat England 1-0 in Sunday's final on Sunday.
Rubiales kissed Jenni Hermoso on the lips, kissed several players on the cheek and embraced them tightly when handing out the medals.
Having initially minimised the outrage, calling critics "idiots", Rubiales said in a video statement sent by the federation: "I was wrong, I have to admit. It was without bad faith at a time of maximum effusiveness."
However, acting Prime Minister Pedro Sanchez said, "We've seen his apology and that's not enough, he must be much clearer and convincing in apologising.
"He must take more steps to clarify a behaviour that is unacceptable."
Sanchez, speaking at a news conference on Tuesday, said the federation was not part of the Spanish government, which lacked the power to appoint or fire the federation's president.
Hermoso told teammates afterwards in the locker room that she "didn't like it," according to video footage posted on Instagram and YouTube by El Mundo newspaper and other media outlets.
She later downplayed the incident in a statement issued by the federation.
"It was a mutual gesture that was totally spontaneous prompted by the huge joy of winning a World Cup," the statement said. "The 'presi' and I have a great relationship, his behaviour with all of us has always been 10 (out of 10) and this was a natural gesture of affection and gratitude."
A non-consensual kiss is "a kind of sex violence all women suffer daily, which was until now invisible, and which we cannot normalise", acting Gender Equality Minister Irene Montero said on social messaging platform X, formerly known as Twitter.
Acting Social Rights Minister Ione Belarra, who belongs to Montero's party, asked "if they do that with all of Spain watching, what might they do privately?"
An opinion column in Spain's top-selling El Pais newspaper on Monday morning was titled: "Jenni didn't like the kiss and we didn't either" - describing it as "an intrusion, an invasion of privacy, an aggression".