The rupee declined 5 paise to 75.49 against the US dollar in opening trade on Wednesday as persistent foreign fund outflows kept the pressure on the local unit.
However, a rally in the domestic equities and sliding crude prices in the international market restricted the rupee's fall, according to forex traders.
The Reserve Bank of India kept the benchmark lending rate unchanged for the ninth time in a row at 4%.
At the interbank foreign exchange, the rupee opened strong at 75.38 but could not hold on to the gains and slipped 5 paise to quote 75.49 against the American dollar in early deals.
In the previous session, the rupee had settled at 75.44 against the greenback.
Fitch Ratings on Wednesday cut India's economic growth forecast to 8.4% for the current fiscal but raised the growth projection for the next financial year to 10.3%.
The dollar index, which gauges the greenback's strength against a basket of six currencies fell 0.22% to 96.16.
On the domestic equity market front, the 30-share Sensex was trading 658.72 points or 1.14 per cent higher at 58,292.37 while the broader NSE Nifty surged 198.15 points or 1.15 per cent to 17,374.85.
Brent crude futures, the global oil benchmark, fell 0.15% to $75.33 per barrel.
Foreign institutional investors remained net sellers in the capital markets, pulling out ₹2,584.97 crore on Tuesday, as per provisional data.