The BRICS group of emerging economies, comprising Brazil, Russia, India, China and South Africa, is due to hold a summit in Johannesburg in August.
At 0815 GMT, the rand traded at 18.4800 against the dollar, about 1% stronger than its previous close.
The International Criminal Court (ICC) issued an arrest warrant in March for Putin, accusing him of the war crime of illegally deporting hundreds of children from Ukraine.
South Africa, as an ICC member, would theoretically be required to arrest Putin if he attends the summit, and a failure to do so could fuel tensions with the West.
South Africa-based financial experts on Tuesday questioned whether Putin would now want to attend the Johannesburg summit after the aborted mutiny by Russian mercenary chief Yevgeny Prigozhin on Saturday that appeared to reveal cracks in the chief's grip on power.
"This coup attempt may have happened at the perfect time for SA to defuse the situation in that it may well encourage Russian President Putin to stay at home and render any debates around whether SA would arrest him, should he arrive, null and void," ETM Analytics said in a research note.
Also supporting the rand was a softer dollar on global markets and less-intense power cuts by state utility Eskom, after an improvement in its generation capacity.
Many South Africans were facing power cuts of around 10 hours a day until recently, but there have been some signs of improvement in the last few weeks as the country grapples with its worst power crisis on record.
On the Johannesburg Stock Exchange, the blue-chip Top-40 index traded 0.7% stronger.
South Africa's benchmark 2030 government bond also firmed, with the yield down 8 basis points to 10.525%.
Statistics South Africa will at 0930 GMT publish first-quarter formal-sector employment figures.
(Reporting by Tannur Anders; Additional reporting by Nellie Peyton; Editing by Alexander Winning and Sherry Jacob-Phillips)
