At 1505 GMT, the rand traded at 14.9900 against the dollar, 0.91% stronger than its previous close and adding to gains made on Monday.
The rand was supported as risk appetite in global markets lifted broadly, with the dollar holding steady near the previous session's five-day low.
Risk-related currencies also benefited from rising commodity prices. South Africa is the world's biggest producer of platinum and chrome and a leading producer of gold and diamonds.
The rand's gains were despite data showing headline unemployment hit a record high of 34.4% in the second quarter as businesses shed staff due to the devastating economic impact of COVID-19.
Market attention globally is focused on the Jackson Hole conference on Friday, at which some investors expect U.S. Federal Reserve Chair Jerome Powell to give hints on a possible timeline for tapering of monetary stimulus.
"Although markets are expecting more details around QE tapering, other factors such as a less hawkish stance from (Fed member Robert Kaplan), weaker than forecasted U.S. Manufacturing PMI data, as well as the rebound in commodities, all allowed for a 'risk-on' mood," said DailyFX analyst Warren Venketas.
Stocks on the Johannesburg Stock Exchange (JSE) continued their positive run on Tuesday as a resurgence of coronavirus cases across the globe kept in check investor worries of tapering by the Federal Reserve on Friday.
The blue-chip top-40 companies index closed up 1.02% at 61,180 points and the all-share index closed up 0.93% at 67,452 points.
The market rally, which saw the indexes making up on some of their heavy losses seen last week, was led by South African banks and industrials.
Naspers and its subsidiary Prosus, which are index heavyweights, gained more than 3%, pushing the industrials index up by 1.11%. Petrochemicals major Sasol Ltd closed up over 6% on rising crude oil prices.
South African government bonds were a touch stronger, with the yield on the 2030 instrument dipping 1.5 basis point to 8.865%.
(Reporting by Olivia Kumwenda-Mtambo and Promit Mukherjee; Editing by David Holmes)
