"How could we have paid a bribe for votes four years after we had won the bid?" president of the South African Football Association (SAFA) Danny Jordaan told South Africa's Sunday Independent newspaper.
"I haven't paid a bribe or taken a bribe from anybody in my life. We don't know who is mentioned there (in the indictment)," he added.
A US indictment said that in 2008, bundles of cash in a briefcase were earlier allegedly handed over at a Paris hotel as a bribe by a "high-ranking South African bid committee official".
Warner was among 14 people indicted by the United States on Wednesday, and is alleged to have sought and accepted bribes during the bidding process for the 1998 and 2010 World Cups in France and South Africa.
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Jordaan, who was president of South Africa's 2010 Local Organising Committee, said the $10 million payment was made to CONCACAF.
The payment, he said, was South Africa's contribution towards CONCACAF's football development fund.
Thabo Mbeki, who was president when South Africa won the bid in 2004, becoming the first African country to host the World Cup, also denied that a bribe was paid by his government.
"I am not aware of anybody who solicited a bribe from the government for the purpose of our country being awarded the right to host the World Cup," he said in statement, adding "no public money was ever used to pay a bribe."