The rupee gained 8 paise to 81.70 against the US dollar in early trade on Monday tracking the weakness of the American currency in the overseas market.
Forex traders said significant foreign fund inflows and crude oil prices below USD 75 a barrel also supported the local unit.
At the interbank foreign exchange, the domestic unit opened strong at 81.76 against the dollar and then rose to 81.70, registering a rise of 8 paise over its previous close.
On Thursday, the rupee closed at 81.78 against the US currency.
The forex market was shut on Friday on account of Buddha Purnima.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, fell 0.07 per cent to 101.14.
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Brent crude futures, the global oil benchmark, advanced 0.07 per cent to USD 75.35 per barrel.
Rupee is likely to remain range bound as RBI intervened from both sides, Finrex Treasury Advisors LLP Head of Treasury Anil Kumar Bhansali said.
"Forex reserves moved towards USD 589 billion, clearly indicating that RBI has been buying dollars and gold from the market. Market awaits for Eurozone Industrial Production and US consumer Inflation Expectation data," Bhansali said.
India's foreign exchange reserves jumped USD 4.532 billion to USD 588.78 billion for the week ended April 28, the Reserve Bank of India said on Friday.
The overall reserves had dropped USD 2.164 billion to USD 584.248 billion in the previous week.
Foreign Institutional Investors (FIIs) were net buyers in the capital market on Friday as they purchased shares worth Rs 777.68 crore, according to exchange data.
In the domestic equity market, the 30-share BSE Sensex advanced 447.03 points or 0.73 per cent to 61,501.32. The broader NSE Nifty rose 120.65 points or 0.67 per cent to 18,189.65.
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