Rupee trading at 55.35/36, little changed from its previous close of 55.3550/3650, as dollar demand from oil firms offsets the selling seen due to gains in the euro and other Asian currencies.
Euro eases versus the dollar but stays close to the four-month peak reached on Friday. Most Asian currencies trading stronger versus the dollar.
The Sensex is trading up 0.2 percent.
"The USD/INR pair will hold in a 55.25 to 55.50 range today. Despite the euro going up, the USD is well bid in the local market by oil firms," a senior dealer with a state-run bank said.