Rupee forwards were active, with the spot-next or three-day forwards ending at 152.70/80 per dollar, compared with Monday's close of 152.60/70.
The spot rupee did not trade on Tuesday.
The central bank fixed the spot rupee reference rate at 152.10 on May 5.
Central Bank Governor Indrajit Coomaraswamy said last week that the monetary authority did not want to allow the rupee to fall "too quickly", but suggested further weakness in the exchange rate was on the cards as policymakers sought a competitive currency.
The downward adjustment to the spot currency was to make the rupee more competitive, he added.
The central bank has allowed the currency to gradually depreciate since mid-December, revising its spot reference rate multiple times.
"There was a bit of demand (for dollars); the pressure to depreciate was seen," said a currency dealer.
Sri Lanka regained a lucrative European Union trade concession, mainly for its top exports garments, the European Union said on Tuesday, but the facility will be subject to vigorous monitoring as Colombo has yet to fully implement eligible terms.
The announcement helped cap losses in rupee forwards, dealers said.
Currency dealers also said they expected higher dollar liquidity from inflows to help stabilise the rupee.
Sri Lanka drew a blowout response in its return to the international bond market, attracting orders of more than $11 billion from 500 accounts for a $1.5 billion 10-year bond.