FIFA was aware of the sponsors’ unhappiness about being connected with yet another ethical scandal involving world soccer’s leadership and said it would meet with the companies’ representatives privately to discuss their concerns. That meeting took place in August; Coca-Cola, Visa, McDonald’s and Anheuser-Busch InBev were among the companies represented.

Last week, however, Swiss authorities announced that they were investigating Mr. Blatter directly for “suspicion of criminal mismanagement and suspicion of misappropriation” of funds. On Sept. 25, a group of officials from the office of Switzerland‘s attorney general arrived at FIFA headquarters in Zurich and, over the next few hours, interrogated Mr. Blatter at length, searched his office and took boxes of documents.

“Given the events of last week,” Visa said Friday, “it’s clear it would be in the best interests of FIFA and the sport for Sepp Blatter to step down immediately.”

Anheuser-Busch InBev went further in calling for Mr. Blatter to step down, saying that “we believe his continued presence to be an obstacle in the reform process.”

The pressure from corporations could make it harder for Mr. Blatter to hold on to FIFA’s presidency until the special election in February. It is unclear what the companies can do other than express their displeasure through public statements like Friday’s announcements and in private meetings with FIFA’s leadership. Contracts bind the companies to FIFA for years, and their long partnerships are a testament to their eagerness to be associated, if not with FIFA, then at least with global events like the World Cup.

In rejecting the calls for his resignation almost as quickly as they were announced, Mr. Blatter might have been signaling that he was prepared to call the sponsors’ bluffs. He also may be counting on FIFA’s ability to replace them if they withdraw their financial support in the future. When two major corporate partners, Sony and Emirates, publicly ended their sponsorship agreements with FIFA last year, the blow was softened by a deal already in place with the Russian energy giant Gazprom.

Still, keeping his post is not entirely Mr. Blatter’s decision. FIFA’s ethics committee could suspend him, at least provisionally, as a result of the Swiss attorney general’s accusations. That was what the committee did to the officials indicted and arrested in May. And last month, Mr. Blatter’s top deputy, the FIFA general secretary Jérôme Valcke, was relieved of his duties after he was accused in an unrelated ethics investigation.