The major sponsors each issued statements saying Blatter should quit after Swiss criminal proceedings were opened against him last week.
Coca-Cola took the first step, saying: "Every day that passes FIFA's image and reputation continues to tarnish."
McDonald's said Blatter going would be "in the best interest of the game".
The 79-year-old is accused by Swiss prosecutors of signing a contract that was "unfavourable to Fifa" and making a "disloyal payment" to UEFA president Michel Platini but denies any wrongdoing.
In a statement released through his lawyers, Blatter said resigning now "would not be in the best interest of FIFA, nor would it advance the process of reform".
Budweiser's parent company, AB InBev, said it considered Blatter "to be an obstacle in the reform process", while Visa said it would be in "the best interests of FIFA and the sport" for the Swiss to resign immediately.
Blatter was re-elected for a fifth term as president of world football's governing body in May, but the election was overshadowed when seven FIFA officials were arrested in dawn raids at a five-star Zurich hotel at the request of the United States.
The US later indicted 14 current and former FIFA officials and associates on charges of "rampant, systemic, and deep-rooted" corruption following a major inquiry by the Federal Bureau of Investigation.
Blatter then announced he would be stepping down as president, but not until February 2016.