The rupee falls to 53.59/60 versus its previous close of 53.47/48 as oil importers step up dollar purchases to meet month-end import commitments in a holiday-shortened week.
The forex and debt markets will remain closed on Wednesday and Friday for local holidays.
Traders say oil firms also prompted to buy dollars on the back of a fall in global crude oil prices overnight.
Brent futures slip for a sixth day on worries over oil demand growth due to an uncertain global economic outlook, but stay above $109 a barrel with simmering tensions in the Middle East helping stem the slide.
Some demand for the greenback also seen from gold importers, traders say, adding they do not expect the pair to rise above 53.80 as exporters would step in to sell.
