In early trade on Wednesday, the rupee fell 4 pence to 78.17 against the US dollar, after a flat domestic share market and a strong US currency.
However, lower oil prices on the global market strengthened the local currency and limited its decline, according to FX brokers.
The rupee began flat at 78.13 versus the US dollar on the interbank foreign exchange, before slipping to 78.17, a 4 paise drop from the previous finish.
The rupee’s closing price versus the US dollar in the previous session was 78.13.
The 30-share Sensex was down 364.12 points, or 0.69 percent, at 52,167.95 on the domestic equities market, while the larger NSE Nifty was down 123.10 points, or 0.79 percent, at 15,515.70.
The dollar index, which measures the value of the dollar against a basket of six different currencies, increased 0.17 percent to 104.61.
Benchmark Brent crude futures for world crude oil fell 3.47 percent to USD 110.67 a barrel.
According to exchange statistics, foreign institutional investors continued to be net sellers on Tuesday in the capital market, selling shares worth Rs 2,701.21 crore.