Early on Monday, the rupee strengthened versus the US dollar by 24 paise to 81.73 on an uptick in domestic markets.
Foreign capital inflows, according to forex traders, also strengthen the local currency.
The domestic unit started out at the interbank foreign exchange at 81.85 against the dollar before rising to 81.73, representing a gain of 24 paise over its previous close.
On Friday, the rupee closed at 81.97 against the US currency.
The rupee is expected to trade with a bullish bias due to improving global risk sentiment and new foreign fund inflows, according to forex traders.
They said that low crude oil prices and a subdued dollar index may also help the local currency.
The dollar index, which measures the strength of the dollar against a basket of six different currencies, decreased 0.09 percent to 104.43.
The benchmark for global oil, Brent crude futures, saw a 0.70 percent decrease to USD 85.23 per barrel.
The 30-share BSE Sensex increased by 564.81 points or 0.94 percent to 60,373.78 points in the local equities market. The NSE Nifty, a more inclusive index, increased by 166.95 points or 0.95 percent to 17,761.30 points.
According to exchange data, Foreign Institutional Investors (FIIs) were net purchasers on Friday in the capital market, buying shares worth Rs 246.24 crore.
With inputs from Agencies.
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