Forex traders said sustained foreign fund outflows weighed on investor sentiments and restricted the appreciation bias.
At the interbank foreign exchange, the domestic unit opened at 82.41 against the dollar, then gained ground to touch 82.33, registering a rise of 33 paise over its previous close.
On Friday, the rupee settled at 82.66 against the US dollar.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, fell 0.25 per cent to 103.61.
Brent crude futures, the global oil benchmark, rose 1.06 per cent to USD 79.40 per barrel.
In the domestic equity market, the 30-share BSE Sensex was trading 468.29 points or 0.78 per cent higher at 60,368.66. The broader NSE Nifty rose 153.80 points or 0.86 per cent to 18,013.25.
Foreign Institutional Investors (FIIs) were net sellers in the capital markets on Friday as they offloaded shares worth ₹2,902.46 crore, according to exchange data.