The currency continued to face depreciation pressure on expected demand for dollar from importers, dealers said.
The spot rupee closed at 153.55/60, slightly higher compared with Thursday's close of 153.60/70. Sri Lanka's currency and stock markets were closed for a public holiday on Friday.
"There were some inflows from remittances after the long weekend," a currency dealer said, asking not to be named.
"But the rupee will be under pressure given it is the start of seasonal imports and we expect more oil imports this month after the shortage."
Thousands of Sri Lankan motorists have been queuing up for fuel since Friday after the state-run fuel retailer limited supplies following a delay in a fuel shipment and a rejection of another shipment due to the wrong specification.
Currency dealers said the market was also waiting for direction from the central bank's monetary policy rate decision on Tuesday and the national budget scheduled to be unveiled on Thursday.
The central bank is expected to keep its key interest rates steady to support the sluggish economy despite a pick-up in inflation amid strong credit growth, a Reuters poll showed.
The rupee has slipped 2.6 percent so far this year.
The island nation has seen 20.4 billion rupees ($132.86 million) worth net inflows into equities this year as of Thursday's close, and 42.7 billion rupees into government securities as of Nov. 1, official data showed.