While capital outflows weighed on the rupee, positive local stocks helped to limit the fall, a forex dealer said.
At the interbank foreign exchange market, the rupee opened lower at 61.65 a dollar from Monday's close of 61.52 and declined further to a low of 61.7150.
However, the local currency bounced back to a high of 61.4250 before closing at 61.54, a fall of two paise.
The dollar gained overseas after a stronger-than-expected report on US retail sales indicated the Federal Reserve could continue to slow the rate of its monthly bond purchases.
The benchmark 30-share Sensex surged 256.61 points, or 1.22 per cent, to 21,289.49, the highest closing since ending at a record 21,326.42 on December 9. Overseas investors sold shares worth a net Rs 260.88 crore yesterday, according to provisional data.
"The dollar index, which measures the US currency's value against a basket of six major currencies, traded strong throughout the day," said Pramit Brahmbhatt, CEO of Alpari Financial Services (India).
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