The rupee is trading at 55.97/99 from 55.9050/9150 close on Monday on the back of dollar demand from oil firms and other importers, though pair is off a session high of 56.0850, its lowest in more than two weeks.
Traders expect the rupee to stay well bid on continued demand from oil firms, with trading also seen volatile as overall volumes remain low.
BSE Sensex was up 0.9 percent.
Traders are on the lookout for RBI intervention if the rupee falls much lower than the 56 mark, which is not far the record low of 56.52 hit on May 31.