The lowest trade was at 129.00 per dollar, dealers said, before the currency closed at 128.90/129.00, edging down slightly from Friday's close of 128.90/95.
Two dealers said one of the two state-run banks, through which the central bank usually directs the market, sold dollars to ease depreciation pressure.
Dealers said some foreign investors also booked forwards to hedge their exposure, tracking foreign outflows in other Asian peers.
'The rupee is going to remain under pressure until the U.S. treasuries settle. Until such time we are going to see a highly volatile rupee,' a currency dealer said on condition of anonymity.
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.
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.
The local currency has weakened 1.1 percent so far this year, following a 10.7 percent depreciation in 2012 as the central bank opted for a flexible exchange rate regime in February 2012.
The central bank on Monday shrugged off the likelihood of fresh pressure on the rupee, despite the widening of the trade deficit in April.
Sri Lanka's main stock index edged down to a seven-week low with turnover slumping to a six-month low with some retail investors taking profits.
The bourse ended 0.1 percent, or 5.89 points, weaker at 6,149.38, its lowest since May 6 on concerns of a possible pullout by more foreign funds.
The market witnessed net foreign inflows of 47 million rupees ($364,800) on Monday in low foreign activity, extending net foreign buying in shares to 16.25 billion rupees so far this year.
The day's turnover was at 201 million rupees, its lowest since Dec. 24, a fifth of this year's daily average of 1.02 billion rupees.
($1 = 128.8500 Sri Lanka rupees)http://www.xe.com/news/2013/06/24/3409941.htm