The rupee gained 24 paise to 81.73 against the US dollar in early trade on Monday amid a positive trend in domestic equities.
Forex traders said foreign fund inflows also supported the local unit.
At the interbank foreign exchange, the domestic unit opened at 81.85 against the dollar, then climbed to 81.73, registering a rise of 24 paise over its previous close.
On Friday, the rupee closed at 81.97 against the US currency.
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The forex traders said the rupee is likely to trade with a positive bias on improved global risk sentiments and fresh foreign fund inflows.
Moreover, weak crude oil prices and muted dollar index may also support the domestic currency, they added.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, fell 0.09 per cent to 104.43.
Brent crude futures, the global oil benchmark, declined 0.70 per cent to $85.23 per barrel.
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In the domestic equity market, the 30-share BSE Sensex rose 564.81 points or 0.94 per cent to 60,373.78 points. The broader NSE Nifty advanced 166.95 points or 0.95 per cent to 17,761.30 points.
Foreign Institutional Investors (FIIs) were net buyers in the capital market on Friday as they purchased shares worth ₹246.24 crore, according to exchange data.