The rupee resumed lower at Rs 52.80/81 per dollar on the Interbank Foreign Exchange, against its previous close of Rs 52.71/72 per dollar.
It dropped further to 53.13 per dollar before ending at 53.02/03 per dollar.
The domestic currency hovered in a range between Rs 52.76 and Rs 53.13 per dollar during the day.
Month-end dollar demand from importers, mainly oil companies, affected the rupee value against the dollar, a dealer said.
Meanwhile, crude oil was up in Asian trade on Tuesday amid thin trade as West Asian geopolitical tension pushed up long-term prices of the commodity, analysts said.
In morning trade, New York's main contract, light sweet crude for February delivery, was trading two cents higher at $99.70 a barrel.