The central bank allowed the spot rupee to slip 0.15 percent or 20 cents to 133.90, near its record low of 134.10, hit on June 28, 2012, Thomson Reuters data showed.
Since the central bank defended the currency, dealers moved to forwards because the spot rate did not reflect the real market price, dealers said.
Actively traded three-month forwards ended at 137.10/40 per dollar, compared to Monday's close of 136.55/70.
Two-month forwards were unchanged at 135.50/80 per dollar and one-month forwards were steady at 134.70/90, as the central bank prevented the currency from falling, dealers said.
However, a central bank official on condition of anonymity told Reuters that the bank regulator only intervenes in the spot market and never fixes prices in the forwards.
The central bank has allowed the spot to fall 0.75 percent, or by 1 rupee since April 30, to account for broad gains in the dollar and rising credit demand in a low rate environment.
Two dealers said some banks are desperate for dollars and have been asking exporters to convert their dollars.
Exporters have been holding dollars as it is cheaper for them to borrow cheaper rupee loans for their operations locally at lower interest rate, dealers said.
Dealers said the currency would face pressure until either dollar inflows pick up or interest rates rise.
The spot rupee has fallen around 2.1 percent so far this year, according to Thomson Reuters data.
Dealers also said the dollars are sold between 138.50/139.00 at some authorised foreign exchange dealers outside banks.