The spot rupee, which traded at 153.77 per dollar during the day, ended at 153.70/80 per dollar, compared with Friday's close of 153.60/65. The foreign exchange market was closed on Monday for a public holiday.
The currency fell 2.5 percent last year and dropped 3.9 percent in 2016.
"The import demand was heavy today because of the three days of holidays. There had been some inflows but the import demand was there," said a currency dealer.
"The import pressure will be there for a while till the banks sort out the new derivatives regulation of the central bank which has slowed down the forward trading."
Although the rupee lost ground last year, currency dealers say dollar demand has waned slightly, lending support to the domestic currency.