Forex dealers said euro's gains against the American currency in the overseas market also supported the rupee.
The local unit had closed higher at 54.18 against the dollar on Monday.
Forex market was closed yesterday for 'Shivaji Jayanti'.
Meanwhile, the 30-share BSE Sensex rose by 106.70 points, or 0.54%, to 19,742.42 in early trade today.