At the interbank foreign exchange, the rupee opened on a weak note at 74.21 against the dollar, then fell further to 74.25, registering a fall of 10 paise over its previous close.
On Friday, the rupee had settled at 74.15 against the US dollar.
Meanwhile, the dollar index, which gauges the greenback’s strength against a basket of six currencies, was trading up 0.01 per cent at 92.80.
Forex traders said easing crude oil prices and positive domestic equities will limit the depreciation bias of the local unit.
Global oil benchmark Brent crude futures fell 1.75 per cent to USD 69.46 per barrel.
On the domestic equity market front, BSE Sensex was trading 217.1 points or 0.40 per cent higher at 54,494.82, while the broader NSE Nifty advanced 57.25 points or 0.35 per cent to 16,295.45.
Meanwhile, foreign institutional investors were net sellers in the capital market on Friday as they offloaded shares worth Rs 69.37 crore, as per exchange data.