At 0645 GMT the rand was up 0.14% at 14.7900 per dollar from its close of 14.8075 in the previous session, taking most of its direction from Asian currencies.

The U.S. Federal Reserve concludes a two-day meeting concludes on Thursday and is expected to lay the groundwork for a rate cut later this year. That would probably increase demand for emerging-market currencies as investors look for higher- yielding assets.

With no economic data due on Tuesday and the 14.60 technical resistance level a long way off, the rand is set to trade in a narrow range before Wednesday's release of local consumer price figures.

"If, as we suspect, inflation prints below 4.5% for a seventh consecutive month, it will solidify our view for a July cut, with the SARB now signalling its willingness to become more accommodative in response to inflation outcomes," Rand Merchant Bank's Nema Ramkhelawan-Bhana said in a note.

Bonds were also steady, with the yield on the benchmark 10-year government bond down 1 basis point to 8.37%.

In stocks, Old Mutual said on Friday it had terminated the employment of suspended Chief Executive Peter Moyo, following a conflict of interest related to an investment firm he founded.