This is after the greenback's recent bull-run paused, with no obvious direction as U.S. markets are closed for a holiday.
At 0606 GMT, the rand had softened 0.02 percent to 11.6675 per dollar, near the upper end of a recent range between 11.3000 and 11.8000.
Government bonds were weaker in early trade as yields ticked up, with the highly-traded instrument due in 2026 adding 6 basis points to 7.6 percent.
"The past two weeks have seen the rand surge stronger and fail, then run weaker and fail," said John Cairns, market analyst at Rand Merchant Bank, adding that a return to volatility toward the end of the week could push the rand lower.
"Risks are skewed for a renewed test of 11.8900 given the weakness in other risk-currencies, that [and] the market is closer to the top than the bottom of the range."
South Africa's statistics agency publishes January consumer inflation numbers on Wednesday, with a Reuters poll of economists seeing the annual figure easing to 4.5 percent from 5.3 percent the previous month.