Blatter: Relegation suitable sanction for racism
"It is now up to us to take the adequate steps," Blatter said in an interview with FIFA's website.
"What I feel we should do is give instructions to our national associations and the confederations - specifically to the disciplinary committees - to be very strong.
"It is not enough to give a fine. Playing a game without spectators is one of the possible sanctions, but the best would be the deduction of points and the relegation of a team, because finally the club is responsible for their spectators."
FIFA recently ordered both Bulgaria and Hungary to play their next home World Cup qualifiers behind closed doors because of racist and anti-Semitic behaviour by their fans respectively.
It warned that it could impose tougher sanctions, including a points deduction and disqualification, in case of a repeat.