Stocks fell 0.5 percent to their lowest close in eight weeks.
The rupee ended at 181.75/90 per dollar on Monday, compared with 181.50/65 in the previous session, market sources said. On Jan. 3, the rupee fell to an all-time low of 183.00 against the dollar.
The currency has appreciated 0.6 percent so far this year, Refinitiv data showed.
It fell 19 percent in 2018, making it one of the worst-performing currencies in Asia, according to Refinitiv data, due to heavy foreign outflows.
The International Monetary Fund last week said it would resume discussions for further disbursal of part of a $1.5 billion loan amid investor worries of heavy debt repayments.
Sri Lanka is struggling to repay its foreign loans, with a record $5.9 billion due this year including $2.6 billion in the first three months. The central bank chief said around $5 billion borrowing in the pipeline could help debt repayments.
The rupee has declined 4.8 percent since a political crisis started in October. That crisis had dented investor sentiment and delayed Sri Lanka's borrowing plans. A series of credit rating downgrades have made it harder for Sri Lanka to borrow as it faces record high repayments.
The Colombo Stock Index ended 0.49 percent weaker at 5,958.47 on Monday. The benchmark index lost 5 percent in 2018.
Turnover was 793.3 million rupees ($4.37 million), less than last year's daily average of 834 million rupees.
Foreign investors sold a net 46.9 million rupees worth of shares on Monday. They have been net sellers of 15.8 billion rupees worth of stocks since a political crisis began on Oct. 26.
The bond market saw outflows of 86.7 billion rupees between Oct. 25 and Jan. 16, the latest central bank data showed.
Foreign investors pulled a net 22.8 billion rupees out of stocks last year, while they net sold 159.8 billion rupees from government securities from January through Dec. 26, bourse and central bank showed data. ** For a report on global markets, click here.