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One-day forwards slipped to 131.74/78 from Wednesday's close of 131.72/78 at 0549 GMT.
Dealers said pressure on the currency would remain as exporters adopted a wait-and-see approach.
The rupee has fallen around 4 percent since June 7, after foreign investors started to pull out of Sri Lanka's treasury bonds due to a rise in US treasury yields.
Data from the central bank, which has stopped publishing foreign holdings in long term T-bonds separately since June 28, showed total foreign holdings in government securities rose 1.2 percent between June 5 and Aug. 2, which currency dealers attributed to foreign buying in short term T-bills.
Sri Lanka's main stock index was 0.06 percent or 3.52 points firmer at 6,155.31 at 0618 GMT.