At 1510 GMT, the rand traded at 18.8050 against the dollar, not far from its previous close of 18.7975.

The dollar was up about 0.16% at 103.72 against a basket of currencies, ahead of the Fed's two-day policy meeting starting on Tuesday.

Risk appetite was muted on Monday with an escalation of tensions in the Middle East after three U.S. soldiers were killed in Jordan, said Andre Cilliers, currency strategist at TreasuryONE.

The local focus this week will be on December money supply, budget and trade balance figures.

On the stock market, the Top-40 index closed down 1.04%, while the broader all-share was 0.95% lower.

South Africa's benchmark 2030 government bond was marginally weaker, with the yield up 0.5 basis point to 9.765%.

(Reporting by Bhargav Acharya and Nellie Peyton; Editing by Kirsten Donovan and Alex Richardson)