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Tracking the smart rally in local equities in late-morning deals, the rupee appreciated further by 16 paise to quote at 63.78 against the American unit at 1045 hours.
Sustained dollar selling by exporters and some banks, too, had a positive impact on the rupee, a forex dealer said.
However, firm dollar overseas after strong jobs data announced last weekend and continued capital outflow limited the rupee rise, he added.
At the Interbank Foreign Exchange (Forex) market, the domestic currency resumed better at 63.85 a dollar from last close of 63.94 and moved in a range of 63.77 and 63.92 before being quoted at 63.78 at 1045 hours, a rise of 16 paise, or 0.25%.
Last Friday, it went up 29 paise, or 0.45%.
The benchmark S&P BSE Sensex today rallied further by 281 points, or 1.04%, in late-morning deals while foreign portfolio investors (FPIs) sold shares worth Rs 437.56 crore last weekend, according to provisional data.
The dollar index, a gauge of six other major global rivals, was trading higher by 0.37%.
