The Brazilian Football Confederation (CBF) named this weekend's penultimate round of matches in the Brazilian championship the "Round against Racism".
"The message the body wants to give... is of protest against the intolerance many players suffer on the pitches of various countries and which ought to be vehemently condemned by the whole football universe," the CBF said in a statement.
"Racism is not resolved with a handshake and none of those who suffer it forget it the next day," CBF president Ricardo Teixeira said in the statement.
The statement appeared to rebuff FIFA President Blatter, who said in an interview last week that incidents of racist abuse during a match should be settled with a handshake after the final whistle.
Blatter, surprised by the widespread outrage of his remarks, later apologised publicly.
The CBF, listing several instances of Brazilian players being the object of racism, said that in 2011 alone former Brazil internationals Gilberto Silva and Roberto Carlos and present Brazil players Marcelo and Neymar were among many who had suffered racist insults from fans or opponents.
"It cannot be justified in the heat of a match nor interpreted as the gesture of a fan. It's something intolerable that doesn't mix with sport," Teixeira added.
"People who don't understand football is for everyone and not just for one race should be banned definitively from sport."
Brazil coach Mano Menezes said there should be strong punishment for people guilty of racism.
"It's very easy for a person to shake another's hand after a match to say sorry for an insult towards what [the other] holds most sacred and significant. The solution is to find in existing laws a means to give out a very strong punishment," he said.
Blatter's remarks were strongly criticised in Britain where Sports Minister Hugh Robertson and English Professional Footballers' Association chief executive Gordon Taylor called for his resignation.
