The rupee opened the day weaker at 61.88 to the dollar, dropping by 5 paise from Monday's close of 61.83 to the dollar.
The rupee has remained rangebound in the last few trading sessions, despite a slump in stocks on Monday.
The rupee is expected to have a quiet session in trade in the absence of any major cues. Markets across the globe were trading with a slight negative bias after an oil slump pushed the US Dow Jones lower on Monday.