The rupee was marginally up by 4 paise at 63.66 against the US dollar in early trade on Tuesday at the Interbank Foreign Exchange on increased selling of the American currency by exporters and banks.
Forex dealers said continued capital inflows as well as higher opening in the domestic equity supported the rupee.
However, they said, greenback's strength against other currencies overseas capped the gains.
The rupee had ended 12 paise higher at 63.70 against the American currency in Monday's trade on fresh bouts of dollar selling by banks and exporters amid huge expectations of a rate cut by the Reserve Bank.
Meanwhile, the benchmark BSE Sensex rose 53.54 points, or 0.19%, to 27,902.53 in early trade.