At the interbank forex market, the local unit opened at 73.22 against the US dollar, then inched higher to 73.20 against the greenback, registering a rise of 10 paise over its previous close.
On Monday, the rupee had settled at 73.30 against the American currency.
"However, appreciation bias could be capped amid concerns that rising COVID-19 cases and subsequent lockdowns in some states may hurt economic recovery and cause foreign outflows," Reliance Securities said in a research note.
Most of the Asian currencies were stronger this Tuesday morning and could lift sentiments, the note added.
On the domestic equity market front, the 30-share BSE benchmark Sensex was trading 270.03 points higher at 49,429.35, and the broader NSE Nifty advanced 85.45 points to 14,723.25.
Meanwhile, the dollar index, which gauges the greenback''s strength against a basket of six currencies, rose 0.05 per cent to 92.64.
Brent crude futures, the global oil benchmark, rose 0.76 per cent to USD 62.62 per barrel.
Foreign institutional investors were net sellers in the capital market as they offloaded shares worth Rs 931.66 crore on Monday, according to exchange data.