The issue hit the headlines around the world on Thursday when Kevin-Prince Boateng led the AC Milan team off during a friendly against lower division Pro Patria because of racist chanting by fans.
Boateng said afterwards: "I was angry, sad, shocked. For things like this still to happen in 2013 is a disgrace, not just for Italy, but for football in the whole world.
"I wanted to send out a signal to the world that things cannot go on like this. We need to open our eyes."
However, Abu Dhabi's The National newspaper on Sunday quoted Blatter as saying: "Walk off? No. I don't think that is the solution.
"I don't think you can run away, because eventually you can run away if you lose a match."
However, Blatter also spoke in support of Boateng and called for tougher punishment for clubs whose fans racially abuse footballers.
"This issue is a very touchy subject but I repeat there is zero tolerance of racism in the stadium," he said.
"The only solution is to be very harsh with the sanctions and the sanctions must be a deduction of points or something similar.
"The Italian federation have yet to provide Fifa with the report detailing what exactly has happened and I have just learnt about this, but we have to have no tolerance with racism, absolutely no tolerance. This action is an example that the spectators must behave well."