At 1547 GMT, the rand traded at 13.3900 per dollar, 0.37 percent weaker than its New York close on Monday.
Demand for the rand stalled after the Reserve Bank's surprise decision last Thursday to keep lending rates on hold after cutting by 25 basis points at its July meeting.
"Sentiment towards the rand is still fragile and will only be restored if USD/ZAR and EUR/ZAR can hold below 13.40 and 16.00 this week," Rand Merchant Bank currency analyst John Cairns said.
Cairns said the immediate threat to the rand was risk aversion amid an escalating war of words between North Korea and the US, German Chancellor Angela Merkel's "uninspiring" win in the election and problems facing US President Donald Trump's healthcare reform bid.
"We do not expect these concerns to last for very long, but for now they prohibit any meaningful rand strength," Cairns said.
In fixed income, the yield for the benchmark government bond due in 2026 rose 8.5 basis points to 8.54 percent.
On the bourse, the benchmark Top-40 index was down 1.5 percent at 48,819 points, while the broader All-share index shed 1.4 percent to 55,070 points.
The JSE was closed for trading due to a public holiday on Monday and the local bourse had to play "catch-up" after the events of the weekend, said Cratos Capital equities trader Greg Davies.
Shares in South Africa's largest company Naspers were down 3.2 percent at 2,867.59 rand, following the fortunes of its largest investment - China's Tencent Holdings.
"Tencent is down more than 3 percent since we last traded," said Davies. Chinese regulators on Monday imposed a fine on Tencent for failing to properly censor online content.
Naspers holds a third of Tencent and both the South African e-commerce firm and South Africa's bourse have scaled record highs this year buoyed by the Chinese technology company's strong performance.
The biggest gainer among the blue-chips was AngloGold Ashanti which rose 1.8 percent to 126.77 rand.
"Only gold shares are up and that is mostly on geopolitics," said Davies referring to the sabre rattling between the U.S and North Korea.