"We remain a strong and stable democratic country and there is no immediate danger posed by the alert," State Security Minister David Mahlobo said in a statement emailed to CNN.
The statement said that South African security forces were working with U.S. officials over their concerns and would continue to focus on terrorist threats to ensure the public's safety.
There was "no need to panic," it said.
Mahlobo's statement followed a warning the U.S. Embassy in South Africa issued Saturday that it had received information that terror groups were planning to carry out "near-term" attacks in the country.
The attacks would target "places where U.S. citizens congregate in South Africa, such as upscale shopping areas and malls in Johannesburg and Cape Town," the statement said.
It said the warning came against the backdrop of a call from ISIS to its supporters to "carry out terrorist attacks globally during the upcoming month of Ramadan."
The South African government statement called the terror alert a "standard precautionary communication" from the United States to its citizens.
British government updates advice
Britain's Foreign Office also updated its guidance Saturday for citizens traveling or based in South Africa, saying there was a high threat of terrorism in the country.
The guidance warned that "attacks could be indiscriminate, including in places visited by foreigners such as shopping areas in Johannesburg and Cape Town."
It advised that British citizens "should be vigilant at this time."
Plots around the world
The U.S. State Department updated a worldwide caution in March, saying ISIS and other terrorist groups continue to plan attacks in many areas of the world. It did not specifically mention South Africa.
Last week, the State Department warned of potential terrorist attacks throughout Europe over the summer
, advising that large-scale sporting events such as the Euro 2016 soccer championship in France presented a potential target for ISIS and similar groups.
The ISIS cell that carried out the Paris and Brussels attacks also sought to target the event
, a suspect has told interrogators.
On Monday, the first day of Ramadan, five people were killed in an attack on a Jordanian intelligence agency office
in a refugee camp north of the capital, Amman. No group has claimed responsibility for the attack.
In Germany on Thursday, three Syrian men were arrested on suspicion of planning an attack
that ISIS reportedly ordered. The German attorney general's office said the men wanted to attack the old town in Dusseldorf in western Germany with suicide bombs, guns and explosives.