The rupee ended 0.11pc weaker at 182.20/40 per dollar compared to Monday's close of 182.00/10.
The rupee fell 0.41pc last week.
However, the currency is up 0.22pc this year.
The International Monetary Fund cut its forecast for Sri Lanka's 2019, economic growth to 2.7pc from 3.5pc, as the Easter Sunday attacks on hotels and churches earlier this year dented tourism and broader business activity.
Foreign outflows from government securities, one of the major reasons behind the rupee's recent weakness, may not abate till the end of parliament elections in 2020, some analysts said.
The central bank does not release foreign trade numbers on a daily basis, but weekly data in the past four weeks has shown a steady outflow.
Foreign investors sold government securities worth 439 million rupees in the week ended Sept. 25, data showed, extending the net foreign outflow so far this year to 55.3 billion rupees through Sept. 25, central bank data showed.
The benchmark stock index ended 0.08pc down at 5,733.64.
The bourse fell 0.38pc last week. So far this year, the index has dropped 5.3pc.
The index rose in a couple of sessions last week, after the central bank said on Tuesday that the Monetary Board had ordered banks to reduce interest rates on all loans and advances by at least 200 basis points by Oct. 15.
Equity market turnover was 214.4 million Sri Lankan rupees ($1.18 million), well below this year's daily average of about 658.5 million rupees.
Last year's daily average was 834.0 million rupees.
Foreign investors were net buyers of 4.6 million rupees worth of shares on Tuesday, but they have been net sellers of 2.57 billion rupees of equities so far this year, according to index data.