The spot rupee ended at 154.00/10 per dollar, compared with Monday's close of 153.75/85. The rupee gained 0.2 percent last week.
"There was demand throughout the day from foreign banks and smaller banks for imports. There were remittances, but the demand was heavy," said a currency dealer.
Dealers expect a 2-3 percent depreciation in the rupee and higher volatility this year on account of debt repayment by the government.
Sri Lanka mopped up 80 billion rupees ($520.66 million) on Monday via treasury bonds after raising $470.6 million on Jan.18 via development bonds, the central bank said.
President Maithripala Sirisena's administration must repay an estimated 1.97 trillion rupees ($12.85 billion) in 2018 - a record high - including $2.9 billion of foreign loans, and a total of $5.36 billion in interest.
Foreign investors bought 3.9 billion rupees worth of government securities this year up to Jan. 24, central bank data showed.
The rupee fell 2.5 percent last year and 3.9 percent in 2016.
Sri Lanka's stock, bond and foreign exchange markets are closed on Wednesday for a Buddhist religious holiday. Markets will resume trading on Thursday.