Fifa is to investigate after Spain fans hurled racist abuse at England's black players in Wednesday's friendly.
England's Shaun Wright-Phillips and Ashley Cole were subjected to monkey chants in Madrid, prompting a furious reaction from the Football Association.
In a statement, Fifa said: "We are concerned about the latest surge of racism and harshly condemn this."
The statement added: "(Fifa) will demand explanations from the Spanish football association."
Fifa president Sepp Blatter said football had the potential to be a powerful anti-racist force.
"There is no room whatsoever for racism or discrimination in our sport. On the
contrary, football is a tool for building bridges and nurturing tolerance," he said.
"The world is already too full of conflict that has its roots in racism and discrimination. Football has a positive influence."
Tony Blair joined the criticism of the abuse, with a spokeswoman for the Prime Minister saying he was "very disappointed" by what happened.
"He believes racism has no part to play in sport or in any other matter," she said on Thursday.
The FA's head of media, Adrian Bevington, said earlier on Thursday that his organisation would be sending a letter of complaint to the Spanish Federation, as well as Fifa and Uefa.
"Football as a whole should stand up and express its disgust at what has gone on here. Quite frankly, it's a disgrace."
Sports minister Richard Caborn said: "I will write to my Spanish counterpart to express my outrage. I would like the Spanish FA to condemn the scenes.
"I also expect Fifa and Uefa to fully investigate the issue.
"There is no place for racism in football or modern society, and I strongly believe that action needs to be taken at the highest level."
Spanish sports minister Maria Jesus san Segundo said the country was committed to promoting equality between people of different races.
"Spain condemns any racist manifestations that take place in the sports arena, or any other public place," she said.
"We will very seriously study what can be done especially regarding the re-inforcement of teaching in social values in schools."
England coach Sven-Goran Eriksson said: "It's very bad to hear when people boo players because of the colour of their skin.
"At Lazio four years ago we had some fans who did the same. When things like this happen, then something must be done."
Piara Powar, spokesman for British football's anti-racist organisation Kick It Out, said: "Uefa needs to threaten the Spanish with closure of stadia, with a ban."
The FA had already complained to Uefa after several England U-21 players were targeted in their game on Tuesday and it will now be highlighting the incidents during the senior game.
Captain David Beckham, who plays at the Bernabeu for Real Madrid, admitted the chanting had surprised him.
"I was surprised but it's something the FA and world football are trying to cut out and they are working very hard," he said.