The rupee appreciated by 24 paise to 73.31 against the US dollar in opening trade on Tuesday supported by positive domestic equities amid improving risk appetite.
At the interbank forex market, the local unit opened at 73.32 against the US dollar, then inched higher to 73.31 against the greenback, registering a rise of 24 paise over its previous close.
On Monday, the rupee had settled at 73.55 against the American currency.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, rose 0.18 per cent to 91.20.
"The US dollar extended gains on Tuesday on bets of a faster economic recovery and could cap appreciation bias," Reliance Securities said in a research note.
However, most of the Asian currencies have started weaker this Tuesday morning and could weigh on sentiments, the note added.
On the domestic equity market front, the 30-share BSE benchmark Sensex was trading 516.20 points higher at 50,366.04, and the broader NSE Nifty advanced 144.25 points to 14,905.80.
Foreign institutional investors were net buyers in the capital market as they purchased shares worth Rs 125.15 crore on Monday, according to exchange data.
Brent crude futures, the global oil benchmark, slipped 1.13 per cent to $62.97 per barrel.