Blatter said legal experts at world soccer's governing body would decide in January what measures are needed to strengthen FIFA's anti-racism laws. National soccer federations will then vote on the proposed regulations at FIFA's annual congress next year.
"We need to start to deduct points from the team Blatter said Tuesday. "It could also mean suspension. It could also mean exclusion."
Racial taunting and other incidents have occurred at venues across Europe and Blatter has spoken repeatedly of toughening FIFA's anti-racism code.
Last week he spoke out against Lazio forward Paolo Di Canio for making a fascist salute in a match. He said Di Canio could be expelled from soccer for the gesture.
The former West Ham striker has defended his actions even repeating the salute after being fined for it earlier this season. Italian soccer player Paolo Di Canio was suspended for one game on Tuesday for making a fascist salute to fans during a match.
Di Canio was also fined $11977 by the Italian Soccer League. The 37-year-old forward will miss Lazio's match at Lecce on Wednesday.
"It was a political sentence it was an unjust decision Di Canio told a Rome radio station. "My gesture has nothing to do with political ideologies."
Italian papers ran photos on Dec. 12 showing Di Canio with his arm outstretched as he was being substituted during the second half of Lazio's 2-1 loss to Livorno the previous day.
The arm gesture is associated in Italy with the salute used under the rule of fascist dictator Benito Mussolini.
Italian Premier Silvio Berlusconi who also owns Serie A team AC Milan called Di Canio "an exhibitionist."
That game featured teams whose fans have opposing political allegiances: Lazio fans waved swastika flags while Livorno fans had red Communist flags. Clashes between Livorno fans and police were reported outside the stadium before the game with one officer slightly injured.
Last January Di Canio was photographed making the salute after his team's 3-1 victory over AS Roma a gesture that drew widespread condemnation. He was fined $13400 by the federation but maintained his gesture had no political significance.
Lazio president Claudio Lotito said his club will appeal the fine.
Blatter said the current anti-racism regulations which advise federations to take measures ranging from fines against players to stadium bans for racist fans are insufficient.
Teams that fail to control their players or fans also might be forced to play matches in empty stadiums. But Blatter said new more severe punishments are needed.
"A financial sanction is not an adequate measure he said. "You can always find someone with enough money to pay the fine."
He said each infraction of FIFA's anti-racism rules should be judged on the merits of the individual case. He refused to outline any minimum or automatic punishments.
Earlier this month Hungary's soccer federation fined Ujpest FC $23250 because its fans chanted anti-Semitic slurs during a league match. The federation also suspended the referee for failing to take action.
Last month Messina's Ivory Coast defender Marc Zoro was reduced to tears by Inter Milan fans' racist slurs and boos in the Italian league and threatened to walk off the field. Some Inter Milan supporters shouted racist abuse again in the next match.