Besides, domestic equity markets soaring to new highs and the dollar losing sheen against some other currencies overseas also supported the local unit, traders said.
Yesterday, the rupee had rebounded by 16 paise to end at 63.88 against the US currency on bouts of dollar selling by exporters and banks.
Meanwhile, the benchmark BSE Sensex spurted by 394.88 points, or 1.12 per cent to trade at a new peak of 35,476.70 in opening trade.
Foreign investors put in Rs 625.13 crore on net basis in stocks yesterday, according to the exchange data.
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