The rupee strengthened 21 paise to trade at 68.36 against the US dollar in morning session at the interbank forex market on Tuesday.
Fresh selling of the American unit by exporters and banks and fall in global crude oil prices boosted the domestic currency.
However, strength in dollar overseas, as investors awaited US Federal Reserve Chairman Jerome Powell's first congressional testimony for hints on the pace of interest rate hikes, capped rupee's gains, traders said.
On Monday, the rupee had retreated from a near two-week high by ending 4 paise lower at 68.57 against the US currency.
The benchmark Sensex fell 57.26 points, or 0.16 per cent, to 36,266.41 points in opening trade on Tuesday.