At 0615 GMT, the rand traded at 14.0550 per dollar, not far off its New York close of 14.0500 on Thursday.
Expectations of a July interest rate cut have risen following weak U.S. economic data, helping boost emerging market currencies, and Friday's non-farm payrolls figures for June could cement bets on an easing of policy.
"The focus this week will be on the Federal Reserve interest rate decision, with today's employment data likely to drive market expectations," Bianca Botes, a Treasury partner at Peregrine Treasury Solutions wrote in a note.
"This data, the trade dynamic between the U.S. and both China and the EU, as well as statements by the Federal Reserve will set the scene. Any hint of a less dovish Fed will see the rand give up some of its recent gains."
In fixed income, the yield on the benchmark government bond due in 2026 added 1.5 basis points to 8.09%.