Actively traded one-month forwards ended at 134.80/135.00 per dollar, compared with Monday's close of 134.80/90.
"Importer demand came into the market. The depreciation pressure is rising day by day amid declining interest rates," said a currency dealer asking not to be named.
Yields on treasury bills fell three to 11 basis points (bps), extending their decline to 41-51 bps since the central bank cut key rates on April 15.
Two-week and one-week forwards were steady at 133.90/134.00 and 133.60/70 per dollar, respectively.
The central bank through moral suasion prevented the spot rupee from dropping below 132.90/133.20, a limit it set in February.
Central bank officials were not available for comment.
Currency dealers said political uncertainty has been weighing on investor confidence and putting pressure on the exchange rate after President Maithripala Sirisena's 100-day programme ended on Thursday.
Sirisena, who promised to dissolve parliament after the end of his 100-day programme on April 23, on Monday tabled constitutional reform measures, which are expected to be voted later on Tuesday.
Currency dealers said the rupee would also be under pressure through June as credit growth was expected to hit a peak due to lower interest rates.
Reuters, 2015