The Indian rupee gained 7 paise and touched 74.35 against the US dollar in early trade on Tuesday, tracking positive domestic equities.
Forex traders said the rupee is trading in a narrow range as investors are awaiting cues from the US Fed's policy decision due on Wednesday.
At the interbank foreign exchange, the domestic unit opened at 74.36 against the dollar, then inched higher to 74.35, registering a gain of 7 paise over its previous close.
On Monday, the rupee had settled at 74.42 against the US dollar.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, was trading 0.05 percent down at 92.60, as traders and investors will look to cues from the Fed's policy decision, due on Wednesday.
Asian currencies have started marginally stronger against the greenback this Tuesday morning and could lend support, Reliance Securities said in a research note.
On the domestic equity market front, BSE Sensex was trading 119.08 points or 0.23 percent higher at 52,971.35, while the broader NSE Nifty advanced 49.95 points or 0.32 percent to 15,874.40.
Meanwhile, foreign institutional investors were net sellers in the capital market on Monday as they offloaded shares worth Rs 2,376.79 crore, as per exchange data.
Global oil benchmark Brent crude futures advanced 0.48 percent to USD 74.86 per barrel.