The rise in the rupee was also supported by dollar-selling by exporters and banks and the US unit's weakness against some currencies overseas ahead of US Federal Reserve Monetary policy decision Wednesday, traders said.
At the interbank forex market, the rupee commenced with strength at 71.34 and appreciated further to quote 37 paise higher at 71.19 against the US dollar.
The rupee had gained 34 paise to close at 71.56 against the US dollar Monday as forex market sentiments were driven by the country's narrowing trade deficit in November as also smart gains in domestic equities.
Brent crude, the international benchmark, dropped by 1.22 per cent to 14-month low of USD 58.85 barrel.
The US Federal Reserve's policy decision is expected on December 19, and market is expecting another rate hike, traders said.
However, a lower opening in the domestic equity market capped the gain in the domestic currency.
The benchmark BSE Sensex fell by 170.50 points, 0.47 per cent, to 36,099.57 in early trade.