A higher stock opening and continued foreign inflows made the going easy for the rupee.
However, the dollar's recovery against some currencies overseas restricted the rupee upmove.
On Monday, scripting its second-biggest single-day gain this year, the rupee had zoomed 37 paise to close at a 17-month high of 65.04.
Forex and money markets were closed yesterday for 'Gudi Padwa'.
The benchmark BSE Sensex rose further by 84.92 points, or 0.28 per cent, to 29,494.44 in early trade.