The spot rupee ended at 153.45/50 per dollar, up from Monday's close of 153.50/60.
"There was exporter conversions and exporters are booking forward expecting further appropriation of rupee after the port deal," a currency dealer said, requesting anonymity.
"Import demand was also there. State banks were buying probably to pay the oil bills so I think the appreciation is short-lived."
Central bank Governor Indrajith Coomaraswamy earlier said the rupee was still "over-valued", and that the monetary authority was 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.
Dealers said a port deal signed during the weekend also helped boost sentiment.