At the interbank foreign exchange market, the local unit opened at 83.92 against the American currency, registering a rise of 5 paise over its previous close.
On Tuesday, the rupee rose 3 paise to close at 83.97 against the US dollar.
The dollar index, which gauges the greenback's strength against a basket of six currencies, was up 0.03 % to 102.58 points.
Brent crude, the international benchmark, was trading higher by 0.40 % to USD 77.49 per barrel in futures trade.
The rupee appears to be range-bound for now, caught between global pressures and stronger US economic data on one side, while the RBI stands firm on the other, bolstered by its robust foreign reserves of over USD 700 billion, CR Forex Advisors MD Amit Pabari said.
"As a result, the USDINR pair is expected to trade within a range of 83.80 to 84.05 in the short term," Pabari added.
On the domestic equity market, the 30-share BSE Sensex appreciated 257.05 points, or 0.31 % , to 81,891.86, while the Nifty was up 75.75 points, or 0.3 % , to 25,088.90 points.
Foreign Institutional Investors (FIIs) were net sellers in the capital markets on Tuesday, as they offloaded shares worth Rs 5,729.60 crore, according to exchange data.
The reconstituted rate-setting panel of the Reserve Bank on Monday started deliberations on the next bi-monthly monetary policy.
In the current context, experts feel that the RBI may not follow the US Federal Reserve, which lowered the benchmark rates by 50 basis points, and the central banks of some developed nations, which have reduced the interest rates.
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