The rupee depreciated 38 paise to 81.78 against the US dollar in early trade on Monday, tracking a muted trend in domestic equities and risk-off sentiment among investors.
Besides, surging crude prices in the international market impacted the domestic unit, traders said.
At the interbank foreign exchange, the local currency opened weak at 81.65 against the dollar, then lost further ground to quote at 81.78, registering a loss of 38 paise over its previous close.
The rupee settled 33 paise higher at 81.40 against the dollar on Friday.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, slipped 0.04 per cent to 112.08.
Brent crude futures, the global oil benchmark, surged 2.77 per cent to USD 87.50 per barrel.
In the domestic equity market, the 30-share BSE Sensex was trading 66.60 points or 0.12 per cent lower at 57,360.32, and the broader NSE Nifty fell 12.90 points or 0.08 per cent to 17,081.45.
After infusing funds in the last two months, foreign investors turned sellers again in September, and pulled out Rs 7,600 crore from the Indian equity markets amid a hawkish stance by the US Fed and sharp depreciation in the rupee.