At 0600 GMT the rand advanced 0.28 per cent to 12.1450 per dollar, taking advantage of a defensive greenback to keep the 12.1380 landmark within striking distance.
Greek Prime Minister Alexis Tsipras made a new offer on a reforms package to foreign creditors on Sunday which may pull the country back from the brink of bankruptcy.
The dollar shed 0.25 per cent against a basket of major currencies, opening the way for the rand to test resistance levels beyond 12.14.
"From a technical perspective the rand is in another corrective phase," said Warrick Butler, chief currency dealer at Standard Bank.
"If the rand manages to break below 12.1350 today then the chances are good for further corrective action to 12.05 and even 11.98," Warrick said in a morning market note.
The rand gained 3 per cent against the dollar last week. Data risks to further progress this week are current account figures on Tuesday and producer inflation on Thursday.
Government bonds were little changed, with the benchmark issue due in 2026 unchanged at 8.39 per cent.
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