At the interbank foreign exchange, the domestic unit opened at 82.21 against the dollar, then gained further ground to touch 82.08, a gain of 22 paise over its previous close.
On Monday, the rupee depreciated by 11 paise to close at 82.30 against the US dollar.
The rupee started stronger this Tuesday, tracking an overnight fall in the dollar index, said Sriram Iyer, Senior Research Analyst at Reliance Securities.
"RBI's continued presence in the markets and oil prices have stabilised and could aid sentiments," Iyer said, adding that Asian and emerging market peers remained weak this Tuesday morning amid recessionary fears and could cap appreciation bias for the local unit.
The dollar index, which gauges the greenback's strength against a basket of six currencies, rose 0.10 per cent to 112.15.
In the domestic equity market, the 30-share BSE Sensex was trading 580.07 points or 0.99 per cent up at 58,991.05. Similarly, the broader NSE Nifty rose 167.85 points or 0.97 per cent to 17,479.65.
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