At 08:47, the rand was at R10.0975/$, compared with a R10.0790 close in New York on Friday.
The rand was trading in a range tested last week when it tried to break through resistance in the R10.0500 region and head for the psychologically key R10/$ area.
"Bullish global markets and a relatively empty international data calendar suggest this could be a positive week for the rand," said John Cairns of Rand Merchant Bank.
"The immediate task is for dollar/rand to break through the 10.05/08 support area, which would open up moves sub-10.00 for the first time since October."
The rand's course will be directed partly by local data such as GDP figures for the third quarter on Tuesday and October trade numbers on Friday afternoon.
Yields on government bonds were up 3 basis points to 8.215% on the benchmark 2026 bond and 2 basis points on the shorter-dated 2015 issue.