The lowest trade was at 129.00 per dollar, but one of the two state-run banks, through which the central bank usually directs the market, sold dollars to selected banks to ease depreciation pressure, dealers said.
The currency closed at 128.70/80, edging up from Monday's close of 128.90/129.00.
'Foreign investors are basically booking their profits in treasury bonds and locking in short term T-bills,' a currency dealer said on condition of anonymity.
'Going forward, we expect the depreciation pressure to remain until the market sees inflows from scheduled foreign borrowings by some banks.'
Foreign investors have been shifting to treasury bills while selling longer tenure T-bonds, the latest central bank data showed on Friday, as a rise in U.S. treasury yields has prompted many offshore investors to rush to the exits.
Three local banks have planned to borrow up to $1.5 billion by tapping global capital markets.
The rupee fell 0.33 percent last week, after losing 1.6 percent in the week previous to that, which currency dealers attributed to foreign investors selling debt as part of a broader selloff in emerging markets.
Sri Lanka's main stock index fell 1.03 percent or 63.16 points to 6,086.22, its lowest since May 3 on concerns over a possible pullout by more foreign funds.
The market witnessed net foreign outflows of 38.7 million rupees on Tuesday in thin foreign trading. The bourse has seen a net foreign inflow of 16.21 billion rupees so far this year.
The day's turnover was at 455.4 million rupees ($3.53 million), less than the half of this year's daily average of around 1 billion rupees.
($1 = 128.9000 Sri Lanka rupees)