By 5pm, the rand traded at R13.2878 to the dollar, 0.8 percent firmer from its New York close on Monday, which was a public holiday in South Africa.
The Fed is due to release its policy statement on Wednesday evening, with the central bank widely expected to leave interest rates unchanged.
In fixed income, the yield for the benchmark government bond due in 2026 dropped.
Gold prices fell on Tuesday to a new three-week low, bringing losses since the start of the week to more than 1 percent, as the dollar hit a six-week peak against the yen.
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Spot gold was down 0.2 percent at $1 254 (R16 735) an ounce at 4.30pm on Tuesday, having earlier hit $1 251.37 an ounce, the lowest since April 10.