At the interbank foreign exchange, the domestic unit opened at 82.05, then fell to 82.08, registering a decline of 7 paise over its last close.
On Tuesday, the rupee had settled at 82.01 against the dollar.
The dollar index, which gauges the greenback's strength against a basket of six currencies, rose 0.08 per cent to 103.12.
Brent crude futures, the global oil benchmark, fell 0.59 per cent to USD 75.80 per barrel.
"Rupee has been ranged in the past few days with dips to the USD getting bought by RBI/oil companies. In-flows continue to be showing strong momentum as FPIs continue to be in a strong buying mode in respect of equities and debt," said Anil Kumar Bhansali, Head of Treasury and Executive Director
Bhansali further noted that the
In the domestic equity market, the 30-share BSE Sensex was trading 70.76 points or 0.11 per cent lower at 65,408.29. The broader NSE Nifty declined 13.90 points or 0.07 per cent to 19,375.10.