The rupee also reached a low of 82.61 versus the dollar in early trade.
In early trade on Tuesday, the rupee strengthened 13 paise to 82.57 against the US dollar after the greenback declined from recent highs.
New foreign capital inflows and a bullish trend in local shares, according to forex traders, also helped to boost investor morale.
The native currency at the interbank foreign exchange started off at 82.59 versus the dollar before moving up and reaching 82.57, rising 13 paise from its previous closing.
The rupee also reached a low of 82.61 versus the dollar in early trade.
The rupee lost 12 paise on Monday to end the day at 82.70 versus the US dollar.
The dollar index, which measures the strength of the dollar against a basket of six different currencies, decreased 0.16 percent to 103.18.
The benchmark for world oil, Brent crude futures, fell 0.70 percent to USD 86 per barrel.
The 30-share BSE Sensex was trading 315.74 points, or 0.52 percent, higher at 60,747.58 on the domestic equities market. The NSE Nifty index as a whole increased by 37.75 points, or 0.21 percent, to 17,808.65.
According to exchange statistics, Foreign Institutional Investors (FIIs) were net purchasers on Monday in the capital market, buying shares worth Rs 1,322.39 crore.
“Global investors will now heed the US consumer inflation data, which is scheduled for release on Tuesday after Asian market hours.
The currency, bond, and equities markets will all be paying careful attention to this print, according to Sriram Iyer, Senior Research Analyst at Reliance Securities. “An upward surprise on inflation will be a concern and will push the Fed to stay higher and for a longer length of time,” he said.
Retail inflation in January again exceeded the Reserve Bank’s upper tolerance level and reached a three-month high of 6.52%, mostly as a result of rising food basket prices, notably those for cereals and protein-rich foods.