80/120.00 levels with weak import demand, dealers said.
In February the central bank's real effective exchange showed the rupee was 26 percent overvalued against the US dollar.
State banks, which usually buy dollars for imports including oil, were less active than usual in the market, dealers said.
State banks also buy to build reserves of the monetary authority.
Central Bank governor Nivard Cabraal said Sri Lanka's central bank which put pressure on the rupee through simultaneous interventions in forex and money markets to defend a peg from September 2008, allowed the rupee to float in late March ahead of an International Monetary Fund bailout.
The central bank says staff level negotiations with the IMF have been finalized.
Before peg defence began the rupee was trading around 108.00 rupees.
The forward premium for dollars had fallen to around 30/35 cents from the 1.
20 rupees seen last month and the 80 cents levels now indicated by the interest rate differential between the US dollars and the rupee at 9.00 percent, dealers said.
A depreciation of the rupee is needed to allow the central bank to collect reserves and also clear an 'overvaluation' of the rupee which is hurting domestic and export industry and slowing economic growth.
The overvaluation is a result of past high inflation generated by the central bank through loose monetary policy (printing money).