At 0640 GMT, the rand traded at 19.0475 against the dollar, near Friday's closing level of 19.0325.
Rand Merchant Bank said in a morning briefing that the exchange rate had looked comfortable around 19 rand to the dollar but that rising U.S. Treasury yields risked pressuring the rand.
ETM Analytics said in a research note that investor concern that the conflict in the Middle East could spread was boosting demand for safe-haven assets.
"This means that the rand will be a price taker, with none of the domestic data scheduled important enough to override these international developments," ETM Analytics said.
Domestic data releases this week including a leading central bank indicator on Tuesday and producer inflation on Thursday.
South Africa's benchmark 2030 government bond was slightly stronger in early deals, the yield down 2 basis points to 10.780%.
(Reporting by Tannur Anders; Editing by Alexander Winning)
