"We remain a strong and stable democratic country and there is no immediate danger," State Security Minister David Mahlobo said in a statement.
The United States on Saturday said it had received information that terrorist groups were planning to carry out attacks in South Africa during the Muslim holy month of Ramadan.
The warning said attacks may target sites frequented by US citizens, including high-end shopping areas and malls in the economic hub of Johannesburg and Cape Town, which is popular with tourists.
One of South Africa's largest shopping centres, Sandton City in Johannesburg, said it was taking the warning seriously.
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Along with several other malls, it is "on high alert and additional security measures have been implemented", said Nomzamo Radebe, CEO of JHI Retail which owns Sandton City.
But the South African government played down the threat.
State security ministry spokesman Brian Dube told AFP that authorities have not stepped up security following the alert.
"Our information has not necessarily confirmed what has been raised by the Americans," he added.