Banks and exporters preferred to reduce their dollar positions on expectations of additional foreign fund flows into the equity market.
The rupee resumed higher at 64.40 a dollar from Friday's close of 65.24 and touched a low of 64.54 at the interbank foreign exchange market.
It later bounced back to breach the 64 mark and touch a high of 63.78 before settling at 63.84, a rise of 140 paise or 2.15 per cent.
Tuesday's rise was the biggest since it added 225 paise on August 29. In four straight sessions, the local currency has flared up by 379 paise or 5.6 per cent.
US jobs data on Friday fell short of expectations, leading to speculation that the tapering of the US Federal Reserve's bond-buying
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