The spot rupee ended at 153.55/60 per dollar, slightly firmer from Monday's close of 153.60/65.
"The market was very dull as everybody is waiting for direction from state banks after they bought dollars," a currency dealer said, asking not to be named.
"There was (dollar) buying by state banks (during the) latter part of the day."
Central Bank Governor Indrajith Coomaraswamy said last week that the rupee was still "over-valued" and that the monetary authority was still buying dollars to avoid any appreciation.
The banking regulator is compelled to buy dollars from the market to meet a reserves target set by the International Monetary Fund (IMF) under a $1.5 billion, three-year loan programme.