Forex dealers said that besides continued selling of the greenback by banks and exporters, a higher opening of the domestic equity market backed the rupee.
On Monday, the rupee had firmed up by 8 paise to close at a near three-week high of 64.36 a dollar on steady selling of the American currency by state-owned banks and exporters.
Meanwhile, the benchmark BSE Sensex rose by 120.83 points, or 0.38 per cent, to 31,430.32 in early trade.
MUMBAI (Agencies) The rupee strengthened by 4 paise to 64.32 against the US dollar in early trade on Tuesday at the Interbank Foreign Exchange market on sustained selling of the American currency by banks and exporters.