Bafana Bafana were supposed to leave for Mexico on Sunday to start preparations for the tournament. The team are set to play co-host Mexico in the opening game in Mexico City on June 11.
South African Sports Minister Gayton McKenzie called the situation "embarrassing" and told the South African Football Association (SAFA) that "I need a report and action must be taken against those responsible for this mess. We are being made to look like fools."
He said later on X that the team would now be departing on Monday.
"All @BafanaBafana players received their visas to travel to the USA, outstanding is assistant coach, team doctor, head of security and one analyst," McKenzie said. "The charter will leave tomorrow."
SAFA had issued a statement earlier on Sunday saying: "The South African senior men's national team has experienced challenges regarding visas for some players and officials, and as a result the group could not travel to North America this morning as originally planned.
"SAFA is working around the clock to ensure that the team travels to Mexico City as soon as possible ahead of the opening match of the global tournament."
The team will continue to train in Johannesburg, South Africa, until departure. SAFA said it would provide an update on the situation after an emergency meeting on Sunday evening.
South Africa also face the Czech Republic and South Korea in Group A.
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