Reuters Market Eye - The rupee falls to 53.72/73 versus its previous close of 53.50/51 due to dollar demand from oil firms that stepped up purchases amid rising global crude prices.
Oil had touched a nine-month peak on Friday, but retreated slightly on Monday.
Traders say volumes are lower than the average with most other Asian markets closed for the Lunar New Year holidays.
The pair has so far moved in a narrow 53.60 to 53.7450 range.
Domestic shares, too, end marginally lower in the absence of any triggers.
The euro's losses against the dollar also help sentiment for the pair.
(Reporting by Swati Bhat)