The dollar losing sheen against some other currencies overseas also supported the local unit, traders said.
Yesterday, the rupee had rebounded by 9 paise to end at 64.37 against the US dollar in a highly volatile trade on fresh selling of the greenback and also emboldened by encouraging Q2 GDP numbers and monthly manufacturing data.
Meanwhile, the benchmark BSE Sensex fell by 108.10 points or 0.32 per cent to 32,761.62 in early trade.