At the interbank foreign exchange market, the local unit opened at 81.43, and witnessed an intra-day high of ₹81.23 and low of ₹81.62 during the session.
The local unit finally settled at 81.47 against the American currency, registering a rise of 45 paise over its previous close.
On Monday, the rupee had settled at 81.92 against the US dollar. The forex market was closed on Tuesday on account of ‘Gurunanak Jayanti’.
Meanwhile, the dollar index, which gauges the greenback’s strength against a basket of six currencies, rose 0.18 per cent to 109.83.
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Global oil benchmark Brent crude futures fell 0.64 per cent to $94.75 per barrel.
“Rupee continued to gain strength as the broader dollar witnessed selling pressure at higher levels. The greenback continued to remain weighed down also ahead of the US mid-term elections results,” said Gaurang Somaiya, Forex and Bullion Analyst, Motilal Oswal Financial Services.
Some market participants suggest a strong chance of Republicans winning a House majority and a tight race for Senate control.
“We expect the USD-INR (Spot) to trade sideways and quote in the range of 81.30 and 81.80,” Somaiya said.
On the domestic equity market front, the 30-share BSE Sensex declined 151.60 points or 0.25 per cent to end at 61,033.55, while the broader NSE Nifty fell 45.80 points or 0.25 per cent to 18,157.00.
Foreign Institutional Investors (FIIs) were net buyers in the capital markets as they purchased shares worth ₹1,948.51 crore on Monday, according to exchange data.