Federal courts have allowed prosecutors to bring cases against foreigners living abroad as long as there is some connection to the United States. Sometimes, that connection is limited, such as the use of an Internet service provider. As a New York prosecutor, Ms. Lynch was aggressive in asserting jurisdiction in cases that reach far outside the country’s border. In the FIFA case, prosecutors say that among other things, soccer officials and other conspirators used American banks in their bribery scheme. Ms. Lynch said she had no qualms about bringing the case on that basis because FIFA was too powerful to go unchecked.

Not everyone cheered the Justice Department’s involvement in the case. President Vladimir V. Putin of Russia denounced the charges, calling them “another blatant attempt by the United States to extend its jurisdiction to other states.”

Mr. Sithole said some South Africans were also suspicious, particularly because the Justice Department was claiming that South Africa had been chosen for the 2010 World Cup at least in part because of bribery. And soccer fans around the world acknowledged surprise that the United States, not known as a major soccer country, had brought the case.

But as they heard details of the allegations in the sweeping indictment — briefcases full of cash, $10 million bribes and fixed votes to determine the site of the World Cup — many said they were happy that someone was finally taking on an institution that has long been considered corrupt.

“Everybody I talk to, we’re just chuffed about this,” Ian Lawrence, a soccer fan from South Wales, said. “It’s the best thing that can happen. If anything, I just wish we’d done it.”

Mr. Lawrence said he had listened to the news conference on the radio, then watched it later at home. He did not know much about the Americans standing behind the microphones, but one thing was clear about Ms. Lynch: “She’s in charge.”

American authorities said that when they began their investigation, they did not anticipate a roundup of FIFA officials. The case was spun off an aspect of an unrelated Russian organized crime investigation, they said. As it progressed, it made its way to Ms. Lynch’s predecessor, Attorney General Eric H. Holder Jr., mostly because of the international issues involved. Prosecutors in Washington worked out the details of the international arrest warrants.