The rupee falls to 55.82/83 from 55.32/33 close on Friday.
However, gains in USD/INR capped by large dollar selling from a major private petrochemical company, traders say.
A senior dealer estimates about $250 million of flows from the company.
The euro slid 1 percent against the yen, hitting its lowest level in more than 11-1/2 years on Monday, pressured by fears that Spain may eventually need a full sovereign bailout.
The Sensex falls 1.3 percent.