Blatter, 76, has been criticised in the past for some of his comments made surrounding discrimination in the game.
He said last month that AC Milan midfielder Kevin-Prince Boateng was wrong to respond to racist abuse during a friendly against Pro Patria by leaving the field.
However, he posted comments on his official Twitter account on Sunday which appear to indicate a hardening of his stance on the issue.
"Sanctions against discriminatory acts must be very severe. We will discuss this at next Strategic Committee in 3 weeks," he wrote on the social media site.
"Deduction of points/team relegation. Financial sanctions: not efficient. Matches behind closed doors: not good solution."
Blatter, who has been president of the sport's world governing body since 1998, courted controversy in November 2011 when he claimed racism did not exist in football and that, if any such issues did arise, they could be solved with a simple handshake.
But the Swiss does now appear to be taking the issue more seriously and he said in December that he intended to meet with his UEFA counterpart Michel Platini to discuss the sanctions handed to the Serbian federation following incidences of racist abuse by supporters during a match against England Under-21s in October.
On December 13, UEFA's control and disciplinary body imposed an 80,000 euro (£65,000) fine and ordered the Serbian Under-21 side to play one match behind closed doors in relation to the racist abuse, but UEFA has subsequently appealed against the leniency of those sanctions.