The former Portsmouth and Tottenham player led his teammates off the pitch during a friendly match with Pro Patria and insisted he would walk-off again in a competitive game under similar circumstances.
Quoted in United Arab Emirates newspaper The National, Blatter said: "Walk off? No. I don't think that is the solution. But the Italian federation has yet to provide FIFA with a report detailing what exactly has happened.
"I don't think you can run away, because then the team should have to forfeit the match. This issue is a very touchy subject, but I repeat there is zero tolerance of racism in the stadium, we have to go against that.
"The only solution is to be very harsh with the sanctions (against racism) - and the sanctions must be a deduction of points or something similar."
AC Milan midfielder Kevin-Prince Boateng has vowed to walk off the field in a competitive football game if he is subjected to any more racial abuse.
The 25-year-old Ghanaian international made world news after storming off the pitch with his teammates during the Italian club's friendly match yesterday, in protest at repeated racial abuse from the stands.
"I don't care what game it is - a friendly, Italian league or Champions League match - I would walk off again," he told CNN today, while calling for life bans for fans who racially abuse players. "If there is a racism those people should be banned from the stadium forever."
The former Premier League player and his teammates received wide praise in the game for their response to the taunts, though former Milan star Clarence Seedorf warned the action may encourage more dissent from fans.