The Guptas were responding to court papers filed last week by Finance Minister Pravin Gordhan which claimed firms linked to the family had made suspect movements worth 6.8 billion rand (USD 490 million).
Their business empire, led by brothers, Atul, Ajay and Rajesh, includes a string of companies, ranging from mining to media.
A total of 72 transactions in companies owned by the family were flagged over four years.
"It is undiluted nonsense and appears to be little more than the usual political games," the Gupta family, who are close to the president, said in a statement.
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The minister filed the records as part of an ongoing court battle over whether he has the power to intervene in a financial dispute involving the family.
Earlier this year several banks and audit firms in South Africa cut ties with Gupta-owned firms.
The family has been lobbying the government to have the banks' decision declared unlawful.
Zuma and Gordhan have clashed in recent months, and Gordhan is due in court next month on separate corruption charges.
The president on Thursday blocked the release of the probe into his relationship with the Guptas, who are accused of having undue influence over government and to have chosen some ministers.