The rupee fell to 54.3450/3500 from its previous close of 54.175/185 in low volume trade as global risk sentiment remained weak after Cyprus bailout.
Dealers said trading interest was also muted as markets will remain closed on Wednesday and Friday for public holidays.
The euro languished near four-month lows against the dollar, held back by fears that future euro zone bank rescues could impose a burden on depositors, while the yen struggled after Japan's central bank chief reaffirmed a commitment to bold easing.
