The rupee rose to 54.78/79 versus its previous close of 54.88/89, and well off a session low at 55.08, as foreign banks continue to sell dollars.
Traders attribute the flows to bunched-up dollar demand as domestic markets were closed for local holidays on Tuesday and Wednesday.
A slight recovery in the euro, after hitting its lowest against the dollar in two months on Tuesday, also pressured the USD/INR cross.
Dollar demand from oil importers, however, is limiting more downside in the pair, dealers say.
The Sensex fell 0.79 percent, marking a two-week closing low after falling for five consecutive sessions.