The central bank on Wednesday cut the spot rupee reference rate by 10 cents to 151.60, dealers said.
Rupee forwards were active, with two-week forwards closing at 152.60/70 per dollar, from Wednesday's close of 152.50/65.
"Market was very light. There was not much activity. There was some demand (for dollar) in the latter part of the day," said a currency dealer who did not wish to be named.
The rupee has been under pressure due to dollar demand to meet increased seasonal imports ahead of the traditional new year that is celebrated on April 13-14, dealers said.
The central bank raised interest rates by 25 basis points on March 24, for the first time in eight months, saying tighter policy was a precaution against a build-up of inflationary pressures.
The rate hike was expected to help stabilise the rupee as rising imports and outflows due to rupee bond sales by foreign investors have exerted pressure on the currency, analysts said.
Foreign investors net sold government securities worth 950 million rupees ($6.26 million) in the week ended March 29. They have net sold 64.2 billion rupees of such instruments so far this year.