The rupee appreciated 16 paise to 79.65 against the US dollar in early trade on Tuesday in line with a positive trend in domestic equities.
At the interbank foreign exchange, the domestic unit opened at 79.70 against the dollar, then touched 79.65, registering a gain of 16 paise over its previous close.
On Monday, the rupee settled 3 paise lower at 79.81 against the dollar.
The dollar index fell 0.15 per cent to 109.57.
Brent crude futures rose 0.11 per cent to $92.10 per barrel.
"Markets were awaiting the US Fed's decision as the two-day meeting starts on Tuesday. A few players expected the US FED to not sound too hawkish lest it hampers the US growth expectations," said Anil Kumar Bhansali, Head of Treasury, Finrex Treasury Advisors.
The Reserve Bank of India will have its Monetary Policy Committee (MPC) meeting between September 28-30, and the outcome will be announced on the last day.
According to Bhansali, the rupee is expected to trade in the range of 79.50-79.90 with risks balanced.
In the domestic equity market, the 30-share BSE Sensex was trading 627.68 points or 1.06 per cent up at 59,768.91. Similarly, the broader NSE Nifty rose 190.80 points or 1.08 per cent to 17,813.05.
Foreign Institutional Investors (FIIs) turned net buyers in the capital markets, as they purchased shares worth ₹312.31 crore on Monday, according to exchange data.