At the interbank foreign exchange market, the local unit opened at 82.20 and touched an intra-day high of 81.72 and a low of 82.26 against the greenback.
It finally ended at 81.78 (provisional), registering a rise of 57 paise over its previous close.
On Monday, the rupee settled at 82.35 against the US dollar.
The dollar index, which gauges the greenback's strength against a basket of six currencies, advanced 0.12 per cent to 103.12.
The rupee became the best performer among the Asian currencies following stop order triggers and inflows from bond selling, said Dilip Parmar, Research Analyst,
"The local unit witnessed the biggest single-day gains after November 11 and broke the psychological level of 82 as the traders rushed to cover the positions," Parmar said.
Parmar further noted that Spot USD/INR now has the support of 81.70, "the 50 per cent Fibonacci retracement adjoining the November 14 low of 80.51 and the January 03 high of 82.94. The near-term view remains bearish for the pair and a level below 81.70 will pave way for 81.45 while on the higher side 82.10 acts as resistance".
On the domestic equity market front, the 30-share BSE Sensex declined 631.83 points or 1.04 per cent to end at 60,115.48, while the broader NSE Nifty fell 187.05 points or 1.03 per cent to 17,914.15.
Global oil benchmark Brent crude futures rose 0.13 per cent to
Foreign Institutional Investors (FIIs) were net sellers in the capital market on Monday as they offloaded shares worth Rs 203.13 crore, according to exchange data.
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