At 0651 GMT the rand was at 10.6740 to the greenback, just 0.2 percent softer than Monday's close. Government debt edged higher, with the yield for paper maturing in 2026 dipping 2 basis points to 8.26 percent.
The yield on the shorter-dated 2015 bond eased to 6.64 percent.
Investor flows were starting to move back into risky assets after last week's sell-off and could nudge dollar/rand towards the 10.64 support level, Standard Bank trader Warrick Butler said.
However, geopolitical tensions in the Middle East, Russia and Iraq would make a recovery in the rand and other risky assets hard to sustain, Barclays Africa said in a note.