The rupee resumed slightly lower at 61.75 as against the last weekend's level of 61.73 per dollar at the Interbank Foreign Exchange market and hovered in the range of 61.75-61.99 before quoting at 61.97 at 1045hrs.
The rupee had gained 39 paise to close at 61.73 against the dollar in yesterday's trade.
Renewed dollar demand from importers mainly affected the rupee value against the dollar, a forex dealer said.
Meanwhile, oil prices edged lower in Asian trade on growing expectations the US Federal Reserve will scale back its stimulus programme after a key policy meeting this week, analysts said.
New York's main contract, West Texas Intermediate (WTI) for January delivery, was down 11 cents at USD 97.37 in early trade.
The benchmark Sensex shot up by 102.76 points or 0.50 pct to 20,762.28 at 1100hrs.