The rupee recovered 21 paise to 72.91 against the US dollar early on Tuesday on increased selling by exporters.
The dollar's weakness against some currencies overseas and a better opening of the domestic equity market also supported the rupee, dealers said.
At the interbank forex market, the rupee opened strong at 72.98 and advanced further to trade at 72.91, reflecting a rise of 21 paise over its previous close of 73.12 against the dollar.
On Monday, the Indian rupee tumbled 67 paise to close at 73.12 against the US dollar on increased demand for the American currency from importers and unabated foreign fund outflows.
Meanwhile, the benchmark Sensex rose 118.44 points, or 0.34 per cent, to 35,069.36 in opening trade on Tuesday.